3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
158 The source of C<isl> can be obtained either as a tarball
159 or from the git repository. Both are available from
160 L<http://freshmeat.net/projects/isl/>.
161 The installation process depends on how you obtained
164 =head2 Installation from the git repository
168 =item 1 Clone or update the repository
170 The first time the source is obtained, you need to clone
173 git clone git://repo.or.cz/isl.git
175 To obtain updates, you need to pull in the latest changes
179 =item 2 Generate C<configure>
185 After performing the above steps, continue
186 with the L<Common installation instructions>.
188 =head2 Common installation instructions
192 =item 1 Obtain C<GMP>
194 Building C<isl> requires C<GMP>, including its headers files.
195 Your distribution may not provide these header files by default
196 and you may need to install a package called C<gmp-devel> or something
197 similar. Alternatively, C<GMP> can be built from
198 source, available from L<http://gmplib.org/>.
202 C<isl> uses the standard C<autoconf> C<configure> script.
207 optionally followed by some configure options.
208 A complete list of options can be obtained by running
212 Below we discuss some of the more common options.
214 C<isl> can optionally use C<piplib>, but no
215 C<piplib> functionality is currently used by default.
216 The C<--with-piplib> option can
217 be used to specify which C<piplib>
218 library to use, either an installed version (C<system>),
219 an externally built version (C<build>)
220 or no version (C<no>). The option C<build> is mostly useful
221 in C<configure> scripts of larger projects that bundle both C<isl>
228 Installation prefix for C<isl>
230 =item C<--with-gmp-prefix>
232 Installation prefix for C<GMP> (architecture-independent files).
234 =item C<--with-gmp-exec-prefix>
236 Installation prefix for C<GMP> (architecture-dependent files).
238 =item C<--with-piplib>
240 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
242 =item C<--with-piplib-prefix>
244 Installation prefix for C<system> C<piplib> (architecture-independent files).
246 =item C<--with-piplib-exec-prefix>
248 Installation prefix for C<system> C<piplib> (architecture-dependent files).
250 =item C<--with-piplib-builddir>
252 Location where C<build> C<piplib> was built.
260 =item 4 Install (optional)
268 =head2 Initialization
270 All manipulations of integer sets and relations occur within
271 the context of an C<isl_ctx>.
272 A given C<isl_ctx> can only be used within a single thread.
273 All arguments of a function are required to have been allocated
274 within the same context.
275 There are currently no functions available for moving an object
276 from one C<isl_ctx> to another C<isl_ctx>. This means that
277 there is currently no way of safely moving an object from one
278 thread to another, unless the whole C<isl_ctx> is moved.
280 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
281 freed using C<isl_ctx_free>.
282 All objects allocated within an C<isl_ctx> should be freed
283 before the C<isl_ctx> itself is freed.
285 isl_ctx *isl_ctx_alloc();
286 void isl_ctx_free(isl_ctx *ctx);
290 All operations on integers, mainly the coefficients
291 of the constraints describing the sets and relations,
292 are performed in exact integer arithmetic using C<GMP>.
293 However, to allow future versions of C<isl> to optionally
294 support fixed integer arithmetic, all calls to C<GMP>
295 are wrapped inside C<isl> specific macros.
296 The basic type is C<isl_int> and the operations below
297 are available on this type.
298 The meanings of these operations are essentially the same
299 as their C<GMP> C<mpz_> counterparts.
300 As always with C<GMP> types, C<isl_int>s need to be
301 initialized with C<isl_int_init> before they can be used
302 and they need to be released with C<isl_int_clear>
304 The user should not assume that an C<isl_int> is represented
305 as a C<mpz_t>, but should instead explicitly convert between
306 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
307 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
311 =item isl_int_init(i)
313 =item isl_int_clear(i)
315 =item isl_int_set(r,i)
317 =item isl_int_set_si(r,i)
319 =item isl_int_set_gmp(r,g)
321 =item isl_int_get_gmp(i,g)
323 =item isl_int_abs(r,i)
325 =item isl_int_neg(r,i)
327 =item isl_int_swap(i,j)
329 =item isl_int_swap_or_set(i,j)
331 =item isl_int_add_ui(r,i,j)
333 =item isl_int_sub_ui(r,i,j)
335 =item isl_int_add(r,i,j)
337 =item isl_int_sub(r,i,j)
339 =item isl_int_mul(r,i,j)
341 =item isl_int_mul_ui(r,i,j)
343 =item isl_int_addmul(r,i,j)
345 =item isl_int_submul(r,i,j)
347 =item isl_int_gcd(r,i,j)
349 =item isl_int_lcm(r,i,j)
351 =item isl_int_divexact(r,i,j)
353 =item isl_int_cdiv_q(r,i,j)
355 =item isl_int_fdiv_q(r,i,j)
357 =item isl_int_fdiv_r(r,i,j)
359 =item isl_int_fdiv_q_ui(r,i,j)
361 =item isl_int_read(r,s)
363 =item isl_int_print(out,i,width)
367 =item isl_int_cmp(i,j)
369 =item isl_int_cmp_si(i,si)
371 =item isl_int_eq(i,j)
373 =item isl_int_ne(i,j)
375 =item isl_int_lt(i,j)
377 =item isl_int_le(i,j)
379 =item isl_int_gt(i,j)
381 =item isl_int_ge(i,j)
383 =item isl_int_abs_eq(i,j)
385 =item isl_int_abs_ne(i,j)
387 =item isl_int_abs_lt(i,j)
389 =item isl_int_abs_gt(i,j)
391 =item isl_int_abs_ge(i,j)
393 =item isl_int_is_zero(i)
395 =item isl_int_is_one(i)
397 =item isl_int_is_negone(i)
399 =item isl_int_is_pos(i)
401 =item isl_int_is_neg(i)
403 =item isl_int_is_nonpos(i)
405 =item isl_int_is_nonneg(i)
407 =item isl_int_is_divisible_by(i,j)
411 =head2 Sets and Relations
413 C<isl> uses six types of objects for representing sets and relations,
414 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
415 C<isl_union_set> and C<isl_union_map>.
416 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
417 can be described as a conjunction of affine constraints, while
418 C<isl_set> and C<isl_map> represent unions of
419 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
420 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
421 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
422 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
423 where spaces are considered different if they have a different number
424 of dimensions and/or different names (see L<"Spaces">).
425 The difference between sets and relations (maps) is that sets have
426 one set of variables, while relations have two sets of variables,
427 input variables and output variables.
429 =head2 Memory Management
431 Since a high-level operation on sets and/or relations usually involves
432 several substeps and since the user is usually not interested in
433 the intermediate results, most functions that return a new object
434 will also release all the objects passed as arguments.
435 If the user still wants to use one or more of these arguments
436 after the function call, she should pass along a copy of the
437 object rather than the object itself.
438 The user is then responsible for making sure that the original
439 object gets used somewhere else or is explicitly freed.
441 The arguments and return values of all documented functions are
442 annotated to make clear which arguments are released and which
443 arguments are preserved. In particular, the following annotations
450 C<__isl_give> means that a new object is returned.
451 The user should make sure that the returned pointer is
452 used exactly once as a value for an C<__isl_take> argument.
453 In between, it can be used as a value for as many
454 C<__isl_keep> arguments as the user likes.
455 There is one exception, and that is the case where the
456 pointer returned is C<NULL>. Is this case, the user
457 is free to use it as an C<__isl_take> argument or not.
461 C<__isl_take> means that the object the argument points to
462 is taken over by the function and may no longer be used
463 by the user as an argument to any other function.
464 The pointer value must be one returned by a function
465 returning an C<__isl_give> pointer.
466 If the user passes in a C<NULL> value, then this will
467 be treated as an error in the sense that the function will
468 not perform its usual operation. However, it will still
469 make sure that all the other C<__isl_take> arguments
474 C<__isl_keep> means that the function will only use the object
475 temporarily. After the function has finished, the user
476 can still use it as an argument to other functions.
477 A C<NULL> value will be treated in the same way as
478 a C<NULL> value for an C<__isl_take> argument.
484 Identifiers are used to identify both individual dimensions
485 and tuples of dimensions. They consist of a name and an optional
486 pointer. Identifiers with the same name but different pointer values
487 are considered to be distinct.
488 Identifiers can be constructed, copied, freed, inspected and printed
489 using the following functions.
492 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
493 __isl_keep const char *name, void *user);
494 __isl_give isl_id *isl_id_copy(isl_id *id);
495 void *isl_id_free(__isl_take isl_id *id);
497 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
498 void *isl_id_get_user(__isl_keep isl_id *id);
499 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
501 __isl_give isl_printer *isl_printer_print_id(
502 __isl_take isl_printer *p, __isl_keep isl_id *id);
504 Note that C<isl_id_get_name> returns a pointer to some internal
505 data structure, so the result can only be used while the
506 corresponding C<isl_id> is alive.
510 Whenever a new set or relation is created from scratch,
511 the space in which it lives needs to be specified using an C<isl_space>.
513 #include <isl/space.h>
514 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
515 unsigned nparam, unsigned n_in, unsigned n_out);
516 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
518 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
519 unsigned nparam, unsigned dim);
520 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
521 void isl_space_free(__isl_take isl_space *space);
522 unsigned isl_space_dim(__isl_keep isl_space *space,
523 enum isl_dim_type type);
525 The space used for creating a parameter domain
526 needs to be created using C<isl_space_params_alloc>.
527 For other sets, the space
528 needs to be created using C<isl_space_set_alloc>, while
529 for a relation, the space
530 needs to be created using C<isl_space_alloc>.
531 C<isl_space_dim> can be used
532 to find out the number of dimensions of each type in
533 a space, where type may be
534 C<isl_dim_param>, C<isl_dim_in> (only for relations),
535 C<isl_dim_out> (only for relations), C<isl_dim_set>
536 (only for sets) or C<isl_dim_all>.
538 To check whether a given space is that of a set or a map
539 or whether it is a parameter space, use these functions:
541 #include <isl/space.h>
542 int isl_space_is_params(__isl_keep isl_space *space);
543 int isl_space_is_set(__isl_keep isl_space *space);
545 It is often useful to create objects that live in the
546 same space as some other object. This can be accomplished
547 by creating the new objects
548 (see L<Creating New Sets and Relations> or
549 L<Creating New (Piecewise) Quasipolynomials>) based on the space
550 of the original object.
553 __isl_give isl_space *isl_basic_set_get_space(
554 __isl_keep isl_basic_set *bset);
555 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
557 #include <isl/union_set.h>
558 __isl_give isl_space *isl_union_set_get_space(
559 __isl_keep isl_union_set *uset);
562 __isl_give isl_space *isl_basic_map_get_space(
563 __isl_keep isl_basic_map *bmap);
564 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
566 #include <isl/union_map.h>
567 __isl_give isl_space *isl_union_map_get_space(
568 __isl_keep isl_union_map *umap);
570 #include <isl/constraint.h>
571 __isl_give isl_space *isl_constraint_get_space(
572 __isl_keep isl_constraint *constraint);
574 #include <isl/polynomial.h>
575 __isl_give isl_space *isl_qpolynomial_get_domain_space(
576 __isl_keep isl_qpolynomial *qp);
577 __isl_give isl_space *isl_qpolynomial_get_space(
578 __isl_keep isl_qpolynomial *qp);
579 __isl_give isl_space *isl_qpolynomial_fold_get_space(
580 __isl_keep isl_qpolynomial_fold *fold);
581 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
582 __isl_keep isl_pw_qpolynomial *pwqp);
583 __isl_give isl_space *isl_pw_qpolynomial_get_space(
584 __isl_keep isl_pw_qpolynomial *pwqp);
585 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
586 __isl_keep isl_pw_qpolynomial_fold *pwf);
587 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
588 __isl_keep isl_pw_qpolynomial_fold *pwf);
589 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
590 __isl_keep isl_union_pw_qpolynomial *upwqp);
591 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
592 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
595 __isl_give isl_space *isl_aff_get_domain_space(
596 __isl_keep isl_aff *aff);
597 __isl_give isl_space *isl_aff_get_space(
598 __isl_keep isl_aff *aff);
599 __isl_give isl_space *isl_pw_aff_get_domain_space(
600 __isl_keep isl_pw_aff *pwaff);
601 __isl_give isl_space *isl_pw_aff_get_space(
602 __isl_keep isl_pw_aff *pwaff);
603 __isl_give isl_space *isl_multi_aff_get_space(
604 __isl_keep isl_multi_aff *maff);
605 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
606 __isl_keep isl_pw_multi_aff *pma);
607 __isl_give isl_space *isl_pw_multi_aff_get_space(
608 __isl_keep isl_pw_multi_aff *pma);
610 #include <isl/point.h>
611 __isl_give isl_space *isl_point_get_space(
612 __isl_keep isl_point *pnt);
614 The identifiers or names of the individual dimensions may be set or read off
615 using the following functions.
617 #include <isl/space.h>
618 __isl_give isl_space *isl_space_set_dim_id(
619 __isl_take isl_space *space,
620 enum isl_dim_type type, unsigned pos,
621 __isl_take isl_id *id);
622 int isl_space_has_dim_id(__isl_keep isl_space *space,
623 enum isl_dim_type type, unsigned pos);
624 __isl_give isl_id *isl_space_get_dim_id(
625 __isl_keep isl_space *space,
626 enum isl_dim_type type, unsigned pos);
627 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
628 enum isl_dim_type type, unsigned pos,
629 __isl_keep const char *name);
630 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
631 enum isl_dim_type type, unsigned pos);
633 Note that C<isl_space_get_name> returns a pointer to some internal
634 data structure, so the result can only be used while the
635 corresponding C<isl_space> is alive.
636 Also note that every function that operates on two sets or relations
637 requires that both arguments have the same parameters. This also
638 means that if one of the arguments has named parameters, then the
639 other needs to have named parameters too and the names need to match.
640 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
641 arguments may have different parameters (as long as they are named),
642 in which case the result will have as parameters the union of the parameters of
645 Given the identifier or name of a dimension (typically a parameter),
646 its position can be obtained from the following function.
648 #include <isl/space.h>
649 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
650 enum isl_dim_type type, __isl_keep isl_id *id);
651 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
652 enum isl_dim_type type, const char *name);
654 The identifiers or names of entire spaces may be set or read off
655 using the following functions.
657 #include <isl/space.h>
658 __isl_give isl_space *isl_space_set_tuple_id(
659 __isl_take isl_space *space,
660 enum isl_dim_type type, __isl_take isl_id *id);
661 __isl_give isl_space *isl_space_reset_tuple_id(
662 __isl_take isl_space *space, enum isl_dim_type type);
663 int isl_space_has_tuple_id(__isl_keep isl_space *space,
664 enum isl_dim_type type);
665 __isl_give isl_id *isl_space_get_tuple_id(
666 __isl_keep isl_space *space, enum isl_dim_type type);
667 __isl_give isl_space *isl_space_set_tuple_name(
668 __isl_take isl_space *space,
669 enum isl_dim_type type, const char *s);
670 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
671 enum isl_dim_type type);
673 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
674 or C<isl_dim_set>. As with C<isl_space_get_name>,
675 the C<isl_space_get_tuple_name> function returns a pointer to some internal
677 Binary operations require the corresponding spaces of their arguments
678 to have the same name.
680 Spaces can be nested. In particular, the domain of a set or
681 the domain or range of a relation can be a nested relation.
682 The following functions can be used to construct and deconstruct
685 #include <isl/space.h>
686 int isl_space_is_wrapping(__isl_keep isl_space *space);
687 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
688 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
690 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
691 be the space of a set, while that of
692 C<isl_space_wrap> should be the space of a relation.
693 Conversely, the output of C<isl_space_unwrap> is the space
694 of a relation, while that of C<isl_space_wrap> is the space of a set.
696 Spaces can be created from other spaces
697 using the following functions.
699 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
700 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
701 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
702 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
703 __isl_give isl_space *isl_space_params(
704 __isl_take isl_space *space);
705 __isl_give isl_space *isl_space_set_from_params(
706 __isl_take isl_space *space);
707 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
708 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
709 __isl_take isl_space *right);
710 __isl_give isl_space *isl_space_align_params(
711 __isl_take isl_space *space1, __isl_take isl_space *space2)
712 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
713 enum isl_dim_type type, unsigned pos, unsigned n);
714 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
715 enum isl_dim_type type, unsigned n);
716 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
717 enum isl_dim_type type, unsigned first, unsigned n);
718 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
719 enum isl_dim_type dst_type, unsigned dst_pos,
720 enum isl_dim_type src_type, unsigned src_pos,
722 __isl_give isl_space *isl_space_map_from_set(
723 __isl_take isl_space *space);
724 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
726 Note that if dimensions are added or removed from a space, then
727 the name and the internal structure are lost.
731 A local space is essentially a space with
732 zero or more existentially quantified variables.
733 The local space of a basic set or relation can be obtained
734 using the following functions.
737 __isl_give isl_local_space *isl_basic_set_get_local_space(
738 __isl_keep isl_basic_set *bset);
741 __isl_give isl_local_space *isl_basic_map_get_local_space(
742 __isl_keep isl_basic_map *bmap);
744 A new local space can be created from a space using
746 #include <isl/local_space.h>
747 __isl_give isl_local_space *isl_local_space_from_space(
748 __isl_take isl_space *space);
750 They can be inspected, modified, copied and freed using the following functions.
752 #include <isl/local_space.h>
753 isl_ctx *isl_local_space_get_ctx(
754 __isl_keep isl_local_space *ls);
755 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
756 int isl_local_space_dim(__isl_keep isl_local_space *ls,
757 enum isl_dim_type type);
758 const char *isl_local_space_get_dim_name(
759 __isl_keep isl_local_space *ls,
760 enum isl_dim_type type, unsigned pos);
761 __isl_give isl_local_space *isl_local_space_set_dim_name(
762 __isl_take isl_local_space *ls,
763 enum isl_dim_type type, unsigned pos, const char *s);
764 __isl_give isl_local_space *isl_local_space_set_dim_id(
765 __isl_take isl_local_space *ls,
766 enum isl_dim_type type, unsigned pos,
767 __isl_take isl_id *id);
768 __isl_give isl_space *isl_local_space_get_space(
769 __isl_keep isl_local_space *ls);
770 __isl_give isl_aff *isl_local_space_get_div(
771 __isl_keep isl_local_space *ls, int pos);
772 __isl_give isl_local_space *isl_local_space_copy(
773 __isl_keep isl_local_space *ls);
774 void *isl_local_space_free(__isl_take isl_local_space *ls);
776 Two local spaces can be compared using
778 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
779 __isl_keep isl_local_space *ls2);
781 Local spaces can be created from other local spaces
782 using the following functions.
784 __isl_give isl_local_space *isl_local_space_domain(
785 __isl_take isl_local_space *ls);
786 __isl_give isl_local_space *isl_local_space_from_domain(
787 __isl_take isl_local_space *ls);
788 __isl_give isl_local_space *isl_local_space_intersect(
789 __isl_take isl_local_space *ls1,
790 __isl_take isl_local_space *ls2);
791 __isl_give isl_local_space *isl_local_space_add_dims(
792 __isl_take isl_local_space *ls,
793 enum isl_dim_type type, unsigned n);
794 __isl_give isl_local_space *isl_local_space_insert_dims(
795 __isl_take isl_local_space *ls,
796 enum isl_dim_type type, unsigned first, unsigned n);
797 __isl_give isl_local_space *isl_local_space_drop_dims(
798 __isl_take isl_local_space *ls,
799 enum isl_dim_type type, unsigned first, unsigned n);
801 =head2 Input and Output
803 C<isl> supports its own input/output format, which is similar
804 to the C<Omega> format, but also supports the C<PolyLib> format
809 The C<isl> format is similar to that of C<Omega>, but has a different
810 syntax for describing the parameters and allows for the definition
811 of an existentially quantified variable as the integer division
812 of an affine expression.
813 For example, the set of integers C<i> between C<0> and C<n>
814 such that C<i % 10 <= 6> can be described as
816 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
819 A set or relation can have several disjuncts, separated
820 by the keyword C<or>. Each disjunct is either a conjunction
821 of constraints or a projection (C<exists>) of a conjunction
822 of constraints. The constraints are separated by the keyword
825 =head3 C<PolyLib> format
827 If the represented set is a union, then the first line
828 contains a single number representing the number of disjuncts.
829 Otherwise, a line containing the number C<1> is optional.
831 Each disjunct is represented by a matrix of constraints.
832 The first line contains two numbers representing
833 the number of rows and columns,
834 where the number of rows is equal to the number of constraints
835 and the number of columns is equal to two plus the number of variables.
836 The following lines contain the actual rows of the constraint matrix.
837 In each row, the first column indicates whether the constraint
838 is an equality (C<0>) or inequality (C<1>). The final column
839 corresponds to the constant term.
841 If the set is parametric, then the coefficients of the parameters
842 appear in the last columns before the constant column.
843 The coefficients of any existentially quantified variables appear
844 between those of the set variables and those of the parameters.
846 =head3 Extended C<PolyLib> format
848 The extended C<PolyLib> format is nearly identical to the
849 C<PolyLib> format. The only difference is that the line
850 containing the number of rows and columns of a constraint matrix
851 also contains four additional numbers:
852 the number of output dimensions, the number of input dimensions,
853 the number of local dimensions (i.e., the number of existentially
854 quantified variables) and the number of parameters.
855 For sets, the number of ``output'' dimensions is equal
856 to the number of set dimensions, while the number of ``input''
862 __isl_give isl_basic_set *isl_basic_set_read_from_file(
863 isl_ctx *ctx, FILE *input);
864 __isl_give isl_basic_set *isl_basic_set_read_from_str(
865 isl_ctx *ctx, const char *str);
866 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
868 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
872 __isl_give isl_basic_map *isl_basic_map_read_from_file(
873 isl_ctx *ctx, FILE *input);
874 __isl_give isl_basic_map *isl_basic_map_read_from_str(
875 isl_ctx *ctx, const char *str);
876 __isl_give isl_map *isl_map_read_from_file(
877 isl_ctx *ctx, FILE *input);
878 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
881 #include <isl/union_set.h>
882 __isl_give isl_union_set *isl_union_set_read_from_file(
883 isl_ctx *ctx, FILE *input);
884 __isl_give isl_union_set *isl_union_set_read_from_str(
885 isl_ctx *ctx, const char *str);
887 #include <isl/union_map.h>
888 __isl_give isl_union_map *isl_union_map_read_from_file(
889 isl_ctx *ctx, FILE *input);
890 __isl_give isl_union_map *isl_union_map_read_from_str(
891 isl_ctx *ctx, const char *str);
893 The input format is autodetected and may be either the C<PolyLib> format
894 or the C<isl> format.
898 Before anything can be printed, an C<isl_printer> needs to
901 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
903 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
904 void isl_printer_free(__isl_take isl_printer *printer);
905 __isl_give char *isl_printer_get_str(
906 __isl_keep isl_printer *printer);
908 The behavior of the printer can be modified in various ways
910 __isl_give isl_printer *isl_printer_set_output_format(
911 __isl_take isl_printer *p, int output_format);
912 __isl_give isl_printer *isl_printer_set_indent(
913 __isl_take isl_printer *p, int indent);
914 __isl_give isl_printer *isl_printer_indent(
915 __isl_take isl_printer *p, int indent);
916 __isl_give isl_printer *isl_printer_set_prefix(
917 __isl_take isl_printer *p, const char *prefix);
918 __isl_give isl_printer *isl_printer_set_suffix(
919 __isl_take isl_printer *p, const char *suffix);
921 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
922 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
923 and defaults to C<ISL_FORMAT_ISL>.
924 Each line in the output is indented by C<indent> (set by
925 C<isl_printer_set_indent>) spaces
926 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
927 In the C<PolyLib> format output,
928 the coefficients of the existentially quantified variables
929 appear between those of the set variables and those
931 The function C<isl_printer_indent> increases the indentation
932 by the specified amount (which may be negative).
934 To actually print something, use
937 __isl_give isl_printer *isl_printer_print_basic_set(
938 __isl_take isl_printer *printer,
939 __isl_keep isl_basic_set *bset);
940 __isl_give isl_printer *isl_printer_print_set(
941 __isl_take isl_printer *printer,
942 __isl_keep isl_set *set);
945 __isl_give isl_printer *isl_printer_print_basic_map(
946 __isl_take isl_printer *printer,
947 __isl_keep isl_basic_map *bmap);
948 __isl_give isl_printer *isl_printer_print_map(
949 __isl_take isl_printer *printer,
950 __isl_keep isl_map *map);
952 #include <isl/union_set.h>
953 __isl_give isl_printer *isl_printer_print_union_set(
954 __isl_take isl_printer *p,
955 __isl_keep isl_union_set *uset);
957 #include <isl/union_map.h>
958 __isl_give isl_printer *isl_printer_print_union_map(
959 __isl_take isl_printer *p,
960 __isl_keep isl_union_map *umap);
962 When called on a file printer, the following function flushes
963 the file. When called on a string printer, the buffer is cleared.
965 __isl_give isl_printer *isl_printer_flush(
966 __isl_take isl_printer *p);
968 =head2 Creating New Sets and Relations
970 C<isl> has functions for creating some standard sets and relations.
974 =item * Empty sets and relations
976 __isl_give isl_basic_set *isl_basic_set_empty(
977 __isl_take isl_space *space);
978 __isl_give isl_basic_map *isl_basic_map_empty(
979 __isl_take isl_space *space);
980 __isl_give isl_set *isl_set_empty(
981 __isl_take isl_space *space);
982 __isl_give isl_map *isl_map_empty(
983 __isl_take isl_space *space);
984 __isl_give isl_union_set *isl_union_set_empty(
985 __isl_take isl_space *space);
986 __isl_give isl_union_map *isl_union_map_empty(
987 __isl_take isl_space *space);
989 For C<isl_union_set>s and C<isl_union_map>s, the space
990 is only used to specify the parameters.
992 =item * Universe sets and relations
994 __isl_give isl_basic_set *isl_basic_set_universe(
995 __isl_take isl_space *space);
996 __isl_give isl_basic_map *isl_basic_map_universe(
997 __isl_take isl_space *space);
998 __isl_give isl_set *isl_set_universe(
999 __isl_take isl_space *space);
1000 __isl_give isl_map *isl_map_universe(
1001 __isl_take isl_space *space);
1002 __isl_give isl_union_set *isl_union_set_universe(
1003 __isl_take isl_union_set *uset);
1004 __isl_give isl_union_map *isl_union_map_universe(
1005 __isl_take isl_union_map *umap);
1007 The sets and relations constructed by the functions above
1008 contain all integer values, while those constructed by the
1009 functions below only contain non-negative values.
1011 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1012 __isl_take isl_space *space);
1013 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1014 __isl_take isl_space *space);
1015 __isl_give isl_set *isl_set_nat_universe(
1016 __isl_take isl_space *space);
1017 __isl_give isl_map *isl_map_nat_universe(
1018 __isl_take isl_space *space);
1020 =item * Identity relations
1022 __isl_give isl_basic_map *isl_basic_map_identity(
1023 __isl_take isl_space *space);
1024 __isl_give isl_map *isl_map_identity(
1025 __isl_take isl_space *space);
1027 The number of input and output dimensions in C<space> needs
1030 =item * Lexicographic order
1032 __isl_give isl_map *isl_map_lex_lt(
1033 __isl_take isl_space *set_space);
1034 __isl_give isl_map *isl_map_lex_le(
1035 __isl_take isl_space *set_space);
1036 __isl_give isl_map *isl_map_lex_gt(
1037 __isl_take isl_space *set_space);
1038 __isl_give isl_map *isl_map_lex_ge(
1039 __isl_take isl_space *set_space);
1040 __isl_give isl_map *isl_map_lex_lt_first(
1041 __isl_take isl_space *space, unsigned n);
1042 __isl_give isl_map *isl_map_lex_le_first(
1043 __isl_take isl_space *space, unsigned n);
1044 __isl_give isl_map *isl_map_lex_gt_first(
1045 __isl_take isl_space *space, unsigned n);
1046 __isl_give isl_map *isl_map_lex_ge_first(
1047 __isl_take isl_space *space, unsigned n);
1049 The first four functions take a space for a B<set>
1050 and return relations that express that the elements in the domain
1051 are lexicographically less
1052 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1053 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1054 than the elements in the range.
1055 The last four functions take a space for a map
1056 and return relations that express that the first C<n> dimensions
1057 in the domain are lexicographically less
1058 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1059 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1060 than the first C<n> dimensions in the range.
1064 A basic set or relation can be converted to a set or relation
1065 using the following functions.
1067 __isl_give isl_set *isl_set_from_basic_set(
1068 __isl_take isl_basic_set *bset);
1069 __isl_give isl_map *isl_map_from_basic_map(
1070 __isl_take isl_basic_map *bmap);
1072 Sets and relations can be converted to union sets and relations
1073 using the following functions.
1075 __isl_give isl_union_map *isl_union_map_from_map(
1076 __isl_take isl_map *map);
1077 __isl_give isl_union_set *isl_union_set_from_set(
1078 __isl_take isl_set *set);
1080 The inverse conversions below can only be used if the input
1081 union set or relation is known to contain elements in exactly one
1084 __isl_give isl_set *isl_set_from_union_set(
1085 __isl_take isl_union_set *uset);
1086 __isl_give isl_map *isl_map_from_union_map(
1087 __isl_take isl_union_map *umap);
1089 A zero-dimensional set can be constructed on a given parameter domain
1090 using the following function.
1092 __isl_give isl_set *isl_set_from_params(
1093 __isl_take isl_set *set);
1095 Sets and relations can be copied and freed again using the following
1098 __isl_give isl_basic_set *isl_basic_set_copy(
1099 __isl_keep isl_basic_set *bset);
1100 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1101 __isl_give isl_union_set *isl_union_set_copy(
1102 __isl_keep isl_union_set *uset);
1103 __isl_give isl_basic_map *isl_basic_map_copy(
1104 __isl_keep isl_basic_map *bmap);
1105 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1106 __isl_give isl_union_map *isl_union_map_copy(
1107 __isl_keep isl_union_map *umap);
1108 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1109 void isl_set_free(__isl_take isl_set *set);
1110 void *isl_union_set_free(__isl_take isl_union_set *uset);
1111 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1112 void isl_map_free(__isl_take isl_map *map);
1113 void *isl_union_map_free(__isl_take isl_union_map *umap);
1115 Other sets and relations can be constructed by starting
1116 from a universe set or relation, adding equality and/or
1117 inequality constraints and then projecting out the
1118 existentially quantified variables, if any.
1119 Constraints can be constructed, manipulated and
1120 added to (or removed from) (basic) sets and relations
1121 using the following functions.
1123 #include <isl/constraint.h>
1124 __isl_give isl_constraint *isl_equality_alloc(
1125 __isl_take isl_local_space *ls);
1126 __isl_give isl_constraint *isl_inequality_alloc(
1127 __isl_take isl_local_space *ls);
1128 __isl_give isl_constraint *isl_constraint_set_constant(
1129 __isl_take isl_constraint *constraint, isl_int v);
1130 __isl_give isl_constraint *isl_constraint_set_constant_si(
1131 __isl_take isl_constraint *constraint, int v);
1132 __isl_give isl_constraint *isl_constraint_set_coefficient(
1133 __isl_take isl_constraint *constraint,
1134 enum isl_dim_type type, int pos, isl_int v);
1135 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1136 __isl_take isl_constraint *constraint,
1137 enum isl_dim_type type, int pos, int v);
1138 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1139 __isl_take isl_basic_map *bmap,
1140 __isl_take isl_constraint *constraint);
1141 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1142 __isl_take isl_basic_set *bset,
1143 __isl_take isl_constraint *constraint);
1144 __isl_give isl_map *isl_map_add_constraint(
1145 __isl_take isl_map *map,
1146 __isl_take isl_constraint *constraint);
1147 __isl_give isl_set *isl_set_add_constraint(
1148 __isl_take isl_set *set,
1149 __isl_take isl_constraint *constraint);
1150 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1151 __isl_take isl_basic_set *bset,
1152 __isl_take isl_constraint *constraint);
1154 For example, to create a set containing the even integers
1155 between 10 and 42, you would use the following code.
1158 isl_local_space *ls;
1160 isl_basic_set *bset;
1162 space = isl_space_set_alloc(ctx, 0, 2);
1163 bset = isl_basic_set_universe(isl_space_copy(space));
1164 ls = isl_local_space_from_space(space);
1166 c = isl_equality_alloc(isl_local_space_copy(ls));
1167 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1168 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1169 bset = isl_basic_set_add_constraint(bset, c);
1171 c = isl_inequality_alloc(isl_local_space_copy(ls));
1172 c = isl_constraint_set_constant_si(c, -10);
1173 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1174 bset = isl_basic_set_add_constraint(bset, c);
1176 c = isl_inequality_alloc(ls);
1177 c = isl_constraint_set_constant_si(c, 42);
1178 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1179 bset = isl_basic_set_add_constraint(bset, c);
1181 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1185 isl_basic_set *bset;
1186 bset = isl_basic_set_read_from_str(ctx,
1187 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1189 A basic set or relation can also be constructed from two matrices
1190 describing the equalities and the inequalities.
1192 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1193 __isl_take isl_space *space,
1194 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1195 enum isl_dim_type c1,
1196 enum isl_dim_type c2, enum isl_dim_type c3,
1197 enum isl_dim_type c4);
1198 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1199 __isl_take isl_space *space,
1200 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1201 enum isl_dim_type c1,
1202 enum isl_dim_type c2, enum isl_dim_type c3,
1203 enum isl_dim_type c4, enum isl_dim_type c5);
1205 The C<isl_dim_type> arguments indicate the order in which
1206 different kinds of variables appear in the input matrices
1207 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1208 C<isl_dim_set> and C<isl_dim_div> for sets and
1209 of C<isl_dim_cst>, C<isl_dim_param>,
1210 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1212 A (basic) set or relation can also be constructed from a (piecewise)
1213 (multiple) affine expression
1214 or a list of affine expressions
1215 (See L<"Piecewise Quasi Affine Expressions"> and
1216 L<"Piecewise Multiple Quasi Affine Expressions">).
1218 __isl_give isl_basic_map *isl_basic_map_from_aff(
1219 __isl_take isl_aff *aff);
1220 __isl_give isl_set *isl_set_from_pw_aff(
1221 __isl_take isl_pw_aff *pwaff);
1222 __isl_give isl_map *isl_map_from_pw_aff(
1223 __isl_take isl_pw_aff *pwaff);
1224 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1225 __isl_take isl_space *domain_space,
1226 __isl_take isl_aff_list *list);
1227 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1228 __isl_take isl_multi_aff *maff)
1229 __isl_give isl_set *isl_set_from_pw_multi_aff(
1230 __isl_take isl_pw_multi_aff *pma);
1231 __isl_give isl_map *isl_map_from_pw_multi_aff(
1232 __isl_take isl_pw_multi_aff *pma);
1234 The C<domain_dim> argument describes the domain of the resulting
1235 basic relation. It is required because the C<list> may consist
1236 of zero affine expressions.
1238 =head2 Inspecting Sets and Relations
1240 Usually, the user should not have to care about the actual constraints
1241 of the sets and maps, but should instead apply the abstract operations
1242 explained in the following sections.
1243 Occasionally, however, it may be required to inspect the individual
1244 coefficients of the constraints. This section explains how to do so.
1245 In these cases, it may also be useful to have C<isl> compute
1246 an explicit representation of the existentially quantified variables.
1248 __isl_give isl_set *isl_set_compute_divs(
1249 __isl_take isl_set *set);
1250 __isl_give isl_map *isl_map_compute_divs(
1251 __isl_take isl_map *map);
1252 __isl_give isl_union_set *isl_union_set_compute_divs(
1253 __isl_take isl_union_set *uset);
1254 __isl_give isl_union_map *isl_union_map_compute_divs(
1255 __isl_take isl_union_map *umap);
1257 This explicit representation defines the existentially quantified
1258 variables as integer divisions of the other variables, possibly
1259 including earlier existentially quantified variables.
1260 An explicitly represented existentially quantified variable therefore
1261 has a unique value when the values of the other variables are known.
1262 If, furthermore, the same existentials, i.e., existentials
1263 with the same explicit representations, should appear in the
1264 same order in each of the disjuncts of a set or map, then the user should call
1265 either of the following functions.
1267 __isl_give isl_set *isl_set_align_divs(
1268 __isl_take isl_set *set);
1269 __isl_give isl_map *isl_map_align_divs(
1270 __isl_take isl_map *map);
1272 Alternatively, the existentially quantified variables can be removed
1273 using the following functions, which compute an overapproximation.
1275 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1276 __isl_take isl_basic_set *bset);
1277 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1278 __isl_take isl_basic_map *bmap);
1279 __isl_give isl_set *isl_set_remove_divs(
1280 __isl_take isl_set *set);
1281 __isl_give isl_map *isl_map_remove_divs(
1282 __isl_take isl_map *map);
1284 To iterate over all the sets or maps in a union set or map, use
1286 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1287 int (*fn)(__isl_take isl_set *set, void *user),
1289 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1290 int (*fn)(__isl_take isl_map *map, void *user),
1293 The number of sets or maps in a union set or map can be obtained
1296 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1297 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1299 To extract the set or map in a given space from a union, use
1301 __isl_give isl_set *isl_union_set_extract_set(
1302 __isl_keep isl_union_set *uset,
1303 __isl_take isl_space *space);
1304 __isl_give isl_map *isl_union_map_extract_map(
1305 __isl_keep isl_union_map *umap,
1306 __isl_take isl_space *space);
1308 To iterate over all the basic sets or maps in a set or map, use
1310 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1311 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1313 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1314 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1317 The callback function C<fn> should return 0 if successful and
1318 -1 if an error occurs. In the latter case, or if any other error
1319 occurs, the above functions will return -1.
1321 It should be noted that C<isl> does not guarantee that
1322 the basic sets or maps passed to C<fn> are disjoint.
1323 If this is required, then the user should call one of
1324 the following functions first.
1326 __isl_give isl_set *isl_set_make_disjoint(
1327 __isl_take isl_set *set);
1328 __isl_give isl_map *isl_map_make_disjoint(
1329 __isl_take isl_map *map);
1331 The number of basic sets in a set can be obtained
1334 int isl_set_n_basic_set(__isl_keep isl_set *set);
1336 To iterate over the constraints of a basic set or map, use
1338 #include <isl/constraint.h>
1340 int isl_basic_map_foreach_constraint(
1341 __isl_keep isl_basic_map *bmap,
1342 int (*fn)(__isl_take isl_constraint *c, void *user),
1344 void *isl_constraint_free(__isl_take isl_constraint *c);
1346 Again, the callback function C<fn> should return 0 if successful and
1347 -1 if an error occurs. In the latter case, or if any other error
1348 occurs, the above functions will return -1.
1349 The constraint C<c> represents either an equality or an inequality.
1350 Use the following function to find out whether a constraint
1351 represents an equality. If not, it represents an inequality.
1353 int isl_constraint_is_equality(
1354 __isl_keep isl_constraint *constraint);
1356 The coefficients of the constraints can be inspected using
1357 the following functions.
1359 void isl_constraint_get_constant(
1360 __isl_keep isl_constraint *constraint, isl_int *v);
1361 void isl_constraint_get_coefficient(
1362 __isl_keep isl_constraint *constraint,
1363 enum isl_dim_type type, int pos, isl_int *v);
1364 int isl_constraint_involves_dims(
1365 __isl_keep isl_constraint *constraint,
1366 enum isl_dim_type type, unsigned first, unsigned n);
1368 The explicit representations of the existentially quantified
1369 variables can be inspected using the following function.
1370 Note that the user is only allowed to use this function
1371 if the inspected set or map is the result of a call
1372 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1373 The existentially quantified variable is equal to the floor
1374 of the returned affine expression. The affine expression
1375 itself can be inspected using the functions in
1376 L<"Piecewise Quasi Affine Expressions">.
1378 __isl_give isl_aff *isl_constraint_get_div(
1379 __isl_keep isl_constraint *constraint, int pos);
1381 To obtain the constraints of a basic set or map in matrix
1382 form, use the following functions.
1384 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1385 __isl_keep isl_basic_set *bset,
1386 enum isl_dim_type c1, enum isl_dim_type c2,
1387 enum isl_dim_type c3, enum isl_dim_type c4);
1388 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1389 __isl_keep isl_basic_set *bset,
1390 enum isl_dim_type c1, enum isl_dim_type c2,
1391 enum isl_dim_type c3, enum isl_dim_type c4);
1392 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1393 __isl_keep isl_basic_map *bmap,
1394 enum isl_dim_type c1,
1395 enum isl_dim_type c2, enum isl_dim_type c3,
1396 enum isl_dim_type c4, enum isl_dim_type c5);
1397 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1398 __isl_keep isl_basic_map *bmap,
1399 enum isl_dim_type c1,
1400 enum isl_dim_type c2, enum isl_dim_type c3,
1401 enum isl_dim_type c4, enum isl_dim_type c5);
1403 The C<isl_dim_type> arguments dictate the order in which
1404 different kinds of variables appear in the resulting matrix
1405 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1406 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1408 The number of parameters, input, output or set dimensions can
1409 be obtained using the following functions.
1411 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1412 enum isl_dim_type type);
1413 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1414 enum isl_dim_type type);
1415 unsigned isl_set_dim(__isl_keep isl_set *set,
1416 enum isl_dim_type type);
1417 unsigned isl_map_dim(__isl_keep isl_map *map,
1418 enum isl_dim_type type);
1420 To check whether the description of a set or relation depends
1421 on one or more given dimensions, it is not necessary to iterate over all
1422 constraints. Instead the following functions can be used.
1424 int isl_basic_set_involves_dims(
1425 __isl_keep isl_basic_set *bset,
1426 enum isl_dim_type type, unsigned first, unsigned n);
1427 int isl_set_involves_dims(__isl_keep isl_set *set,
1428 enum isl_dim_type type, unsigned first, unsigned n);
1429 int isl_basic_map_involves_dims(
1430 __isl_keep isl_basic_map *bmap,
1431 enum isl_dim_type type, unsigned first, unsigned n);
1432 int isl_map_involves_dims(__isl_keep isl_map *map,
1433 enum isl_dim_type type, unsigned first, unsigned n);
1435 Similarly, the following functions can be used to check whether
1436 a given dimension is involved in any lower or upper bound.
1438 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1439 enum isl_dim_type type, unsigned pos);
1440 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1441 enum isl_dim_type type, unsigned pos);
1443 The identifiers or names of the domain and range spaces of a set
1444 or relation can be read off or set using the following functions.
1446 __isl_give isl_set *isl_set_set_tuple_id(
1447 __isl_take isl_set *set, __isl_take isl_id *id);
1448 __isl_give isl_set *isl_set_reset_tuple_id(
1449 __isl_take isl_set *set);
1450 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1451 __isl_give isl_id *isl_set_get_tuple_id(
1452 __isl_keep isl_set *set);
1453 __isl_give isl_map *isl_map_set_tuple_id(
1454 __isl_take isl_map *map, enum isl_dim_type type,
1455 __isl_take isl_id *id);
1456 __isl_give isl_map *isl_map_reset_tuple_id(
1457 __isl_take isl_map *map, enum isl_dim_type type);
1458 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1459 enum isl_dim_type type);
1460 __isl_give isl_id *isl_map_get_tuple_id(
1461 __isl_keep isl_map *map, enum isl_dim_type type);
1463 const char *isl_basic_set_get_tuple_name(
1464 __isl_keep isl_basic_set *bset);
1465 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1466 __isl_take isl_basic_set *set, const char *s);
1467 const char *isl_set_get_tuple_name(
1468 __isl_keep isl_set *set);
1469 const char *isl_basic_map_get_tuple_name(
1470 __isl_keep isl_basic_map *bmap,
1471 enum isl_dim_type type);
1472 const char *isl_map_get_tuple_name(
1473 __isl_keep isl_map *map,
1474 enum isl_dim_type type);
1476 As with C<isl_space_get_tuple_name>, the value returned points to
1477 an internal data structure.
1478 The identifiers, positions or names of individual dimensions can be
1479 read off using the following functions.
1481 __isl_give isl_set *isl_set_set_dim_id(
1482 __isl_take isl_set *set, enum isl_dim_type type,
1483 unsigned pos, __isl_take isl_id *id);
1484 int isl_set_has_dim_id(__isl_keep isl_set *set,
1485 enum isl_dim_type type, unsigned pos);
1486 __isl_give isl_id *isl_set_get_dim_id(
1487 __isl_keep isl_set *set, enum isl_dim_type type,
1489 int isl_basic_map_has_dim_id(
1490 __isl_keep isl_basic_map *bmap,
1491 enum isl_dim_type type, unsigned pos);
1492 __isl_give isl_map *isl_map_set_dim_id(
1493 __isl_take isl_map *map, enum isl_dim_type type,
1494 unsigned pos, __isl_take isl_id *id);
1495 int isl_map_has_dim_id(__isl_keep isl_map *map,
1496 enum isl_dim_type type, unsigned pos);
1497 __isl_give isl_id *isl_map_get_dim_id(
1498 __isl_keep isl_map *map, enum isl_dim_type type,
1501 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1502 enum isl_dim_type type, __isl_keep isl_id *id);
1503 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1504 enum isl_dim_type type, __isl_keep isl_id *id);
1505 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1506 enum isl_dim_type type, const char *name);
1508 const char *isl_constraint_get_dim_name(
1509 __isl_keep isl_constraint *constraint,
1510 enum isl_dim_type type, unsigned pos);
1511 const char *isl_basic_set_get_dim_name(
1512 __isl_keep isl_basic_set *bset,
1513 enum isl_dim_type type, unsigned pos);
1514 const char *isl_set_get_dim_name(
1515 __isl_keep isl_set *set,
1516 enum isl_dim_type type, unsigned pos);
1517 const char *isl_basic_map_get_dim_name(
1518 __isl_keep isl_basic_map *bmap,
1519 enum isl_dim_type type, unsigned pos);
1520 const char *isl_map_get_dim_name(
1521 __isl_keep isl_map *map,
1522 enum isl_dim_type type, unsigned pos);
1524 These functions are mostly useful to obtain the identifiers, positions
1525 or names of the parameters. Identifiers of individual dimensions are
1526 essentially only useful for printing. They are ignored by all other
1527 operations and may not be preserved across those operations.
1531 =head3 Unary Properties
1537 The following functions test whether the given set or relation
1538 contains any integer points. The ``plain'' variants do not perform
1539 any computations, but simply check if the given set or relation
1540 is already known to be empty.
1542 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1543 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1544 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1545 int isl_set_is_empty(__isl_keep isl_set *set);
1546 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1547 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1548 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1549 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1550 int isl_map_is_empty(__isl_keep isl_map *map);
1551 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1553 =item * Universality
1555 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1556 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1557 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1559 =item * Single-valuedness
1561 int isl_map_is_single_valued(__isl_keep isl_map *map);
1562 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1566 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1567 int isl_map_is_injective(__isl_keep isl_map *map);
1568 int isl_union_map_plain_is_injective(
1569 __isl_keep isl_union_map *umap);
1570 int isl_union_map_is_injective(
1571 __isl_keep isl_union_map *umap);
1575 int isl_map_is_bijective(__isl_keep isl_map *map);
1576 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1580 int isl_basic_map_plain_is_fixed(
1581 __isl_keep isl_basic_map *bmap,
1582 enum isl_dim_type type, unsigned pos,
1584 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1585 enum isl_dim_type type, unsigned pos,
1587 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1588 enum isl_dim_type type, unsigned pos,
1591 Check if the relation obviously lies on a hyperplane where the given dimension
1592 has a fixed value and if so, return that value in C<*val>.
1596 To check whether a set is a parameter domain, use this function:
1598 int isl_set_is_params(__isl_keep isl_set *set);
1599 int isl_union_set_is_params(
1600 __isl_keep isl_union_set *uset);
1604 The following functions check whether the domain of the given
1605 (basic) set is a wrapped relation.
1607 int isl_basic_set_is_wrapping(
1608 __isl_keep isl_basic_set *bset);
1609 int isl_set_is_wrapping(__isl_keep isl_set *set);
1611 =item * Internal Product
1613 int isl_basic_map_can_zip(
1614 __isl_keep isl_basic_map *bmap);
1615 int isl_map_can_zip(__isl_keep isl_map *map);
1617 Check whether the product of domain and range of the given relation
1619 i.e., whether both domain and range are nested relations.
1623 =head3 Binary Properties
1629 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1630 __isl_keep isl_set *set2);
1631 int isl_set_is_equal(__isl_keep isl_set *set1,
1632 __isl_keep isl_set *set2);
1633 int isl_union_set_is_equal(
1634 __isl_keep isl_union_set *uset1,
1635 __isl_keep isl_union_set *uset2);
1636 int isl_basic_map_is_equal(
1637 __isl_keep isl_basic_map *bmap1,
1638 __isl_keep isl_basic_map *bmap2);
1639 int isl_map_is_equal(__isl_keep isl_map *map1,
1640 __isl_keep isl_map *map2);
1641 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1642 __isl_keep isl_map *map2);
1643 int isl_union_map_is_equal(
1644 __isl_keep isl_union_map *umap1,
1645 __isl_keep isl_union_map *umap2);
1647 =item * Disjointness
1649 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1650 __isl_keep isl_set *set2);
1654 int isl_set_is_subset(__isl_keep isl_set *set1,
1655 __isl_keep isl_set *set2);
1656 int isl_set_is_strict_subset(
1657 __isl_keep isl_set *set1,
1658 __isl_keep isl_set *set2);
1659 int isl_union_set_is_subset(
1660 __isl_keep isl_union_set *uset1,
1661 __isl_keep isl_union_set *uset2);
1662 int isl_union_set_is_strict_subset(
1663 __isl_keep isl_union_set *uset1,
1664 __isl_keep isl_union_set *uset2);
1665 int isl_basic_map_is_subset(
1666 __isl_keep isl_basic_map *bmap1,
1667 __isl_keep isl_basic_map *bmap2);
1668 int isl_basic_map_is_strict_subset(
1669 __isl_keep isl_basic_map *bmap1,
1670 __isl_keep isl_basic_map *bmap2);
1671 int isl_map_is_subset(
1672 __isl_keep isl_map *map1,
1673 __isl_keep isl_map *map2);
1674 int isl_map_is_strict_subset(
1675 __isl_keep isl_map *map1,
1676 __isl_keep isl_map *map2);
1677 int isl_union_map_is_subset(
1678 __isl_keep isl_union_map *umap1,
1679 __isl_keep isl_union_map *umap2);
1680 int isl_union_map_is_strict_subset(
1681 __isl_keep isl_union_map *umap1,
1682 __isl_keep isl_union_map *umap2);
1686 =head2 Unary Operations
1692 __isl_give isl_set *isl_set_complement(
1693 __isl_take isl_set *set);
1697 __isl_give isl_basic_map *isl_basic_map_reverse(
1698 __isl_take isl_basic_map *bmap);
1699 __isl_give isl_map *isl_map_reverse(
1700 __isl_take isl_map *map);
1701 __isl_give isl_union_map *isl_union_map_reverse(
1702 __isl_take isl_union_map *umap);
1706 __isl_give isl_basic_set *isl_basic_set_project_out(
1707 __isl_take isl_basic_set *bset,
1708 enum isl_dim_type type, unsigned first, unsigned n);
1709 __isl_give isl_basic_map *isl_basic_map_project_out(
1710 __isl_take isl_basic_map *bmap,
1711 enum isl_dim_type type, unsigned first, unsigned n);
1712 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1713 enum isl_dim_type type, unsigned first, unsigned n);
1714 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1715 enum isl_dim_type type, unsigned first, unsigned n);
1716 __isl_give isl_basic_set *isl_basic_set_params(
1717 __isl_take isl_basic_set *bset);
1718 __isl_give isl_basic_set *isl_basic_map_domain(
1719 __isl_take isl_basic_map *bmap);
1720 __isl_give isl_basic_set *isl_basic_map_range(
1721 __isl_take isl_basic_map *bmap);
1722 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1723 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1724 __isl_give isl_set *isl_map_domain(
1725 __isl_take isl_map *bmap);
1726 __isl_give isl_set *isl_map_range(
1727 __isl_take isl_map *map);
1728 __isl_give isl_set *isl_union_set_params(
1729 __isl_take isl_union_set *uset);
1730 __isl_give isl_set *isl_union_map_params(
1731 __isl_take isl_union_map *umap);
1732 __isl_give isl_union_set *isl_union_map_domain(
1733 __isl_take isl_union_map *umap);
1734 __isl_give isl_union_set *isl_union_map_range(
1735 __isl_take isl_union_map *umap);
1737 __isl_give isl_basic_map *isl_basic_map_domain_map(
1738 __isl_take isl_basic_map *bmap);
1739 __isl_give isl_basic_map *isl_basic_map_range_map(
1740 __isl_take isl_basic_map *bmap);
1741 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1742 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1743 __isl_give isl_union_map *isl_union_map_domain_map(
1744 __isl_take isl_union_map *umap);
1745 __isl_give isl_union_map *isl_union_map_range_map(
1746 __isl_take isl_union_map *umap);
1748 The functions above construct a (basic, regular or union) relation
1749 that maps (a wrapped version of) the input relation to its domain or range.
1753 __isl_give isl_set *isl_set_eliminate(
1754 __isl_take isl_set *set, enum isl_dim_type type,
1755 unsigned first, unsigned n);
1756 __isl_give isl_basic_map *isl_basic_map_eliminate(
1757 __isl_take isl_basic_map *bmap,
1758 enum isl_dim_type type,
1759 unsigned first, unsigned n);
1761 Eliminate the coefficients for the given dimensions from the constraints,
1762 without removing the dimensions.
1766 __isl_give isl_basic_set *isl_basic_set_fix(
1767 __isl_take isl_basic_set *bset,
1768 enum isl_dim_type type, unsigned pos,
1770 __isl_give isl_basic_set *isl_basic_set_fix_si(
1771 __isl_take isl_basic_set *bset,
1772 enum isl_dim_type type, unsigned pos, int value);
1773 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1774 enum isl_dim_type type, unsigned pos,
1776 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1777 enum isl_dim_type type, unsigned pos, int value);
1778 __isl_give isl_basic_map *isl_basic_map_fix_si(
1779 __isl_take isl_basic_map *bmap,
1780 enum isl_dim_type type, unsigned pos, int value);
1781 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1782 enum isl_dim_type type, unsigned pos, int value);
1784 Intersect the set or relation with the hyperplane where the given
1785 dimension has the fixed given value.
1787 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1788 __isl_take isl_basic_map *bmap,
1789 enum isl_dim_type type, unsigned pos, int value);
1790 __isl_give isl_set *isl_set_lower_bound_si(
1791 __isl_take isl_set *set,
1792 enum isl_dim_type type, unsigned pos, int value);
1793 __isl_give isl_map *isl_map_lower_bound_si(
1794 __isl_take isl_map *map,
1795 enum isl_dim_type type, unsigned pos, int value);
1796 __isl_give isl_set *isl_set_upper_bound_si(
1797 __isl_take isl_set *set,
1798 enum isl_dim_type type, unsigned pos, int value);
1799 __isl_give isl_map *isl_map_upper_bound_si(
1800 __isl_take isl_map *map,
1801 enum isl_dim_type type, unsigned pos, int value);
1803 Intersect the set or relation with the half-space where the given
1804 dimension has a value bounded the fixed given value.
1806 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1807 enum isl_dim_type type1, int pos1,
1808 enum isl_dim_type type2, int pos2);
1809 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1810 enum isl_dim_type type1, int pos1,
1811 enum isl_dim_type type2, int pos2);
1813 Intersect the set or relation with the hyperplane where the given
1814 dimensions are equal to each other.
1816 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1817 enum isl_dim_type type1, int pos1,
1818 enum isl_dim_type type2, int pos2);
1820 Intersect the relation with the hyperplane where the given
1821 dimensions have opposite values.
1825 __isl_give isl_map *isl_set_identity(
1826 __isl_take isl_set *set);
1827 __isl_give isl_union_map *isl_union_set_identity(
1828 __isl_take isl_union_set *uset);
1830 Construct an identity relation on the given (union) set.
1834 __isl_give isl_basic_set *isl_basic_map_deltas(
1835 __isl_take isl_basic_map *bmap);
1836 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1837 __isl_give isl_union_set *isl_union_map_deltas(
1838 __isl_take isl_union_map *umap);
1840 These functions return a (basic) set containing the differences
1841 between image elements and corresponding domain elements in the input.
1843 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1844 __isl_take isl_basic_map *bmap);
1845 __isl_give isl_map *isl_map_deltas_map(
1846 __isl_take isl_map *map);
1847 __isl_give isl_union_map *isl_union_map_deltas_map(
1848 __isl_take isl_union_map *umap);
1850 The functions above construct a (basic, regular or union) relation
1851 that maps (a wrapped version of) the input relation to its delta set.
1855 Simplify the representation of a set or relation by trying
1856 to combine pairs of basic sets or relations into a single
1857 basic set or relation.
1859 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1860 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1861 __isl_give isl_union_set *isl_union_set_coalesce(
1862 __isl_take isl_union_set *uset);
1863 __isl_give isl_union_map *isl_union_map_coalesce(
1864 __isl_take isl_union_map *umap);
1866 =item * Detecting equalities
1868 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1869 __isl_take isl_basic_set *bset);
1870 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1871 __isl_take isl_basic_map *bmap);
1872 __isl_give isl_set *isl_set_detect_equalities(
1873 __isl_take isl_set *set);
1874 __isl_give isl_map *isl_map_detect_equalities(
1875 __isl_take isl_map *map);
1876 __isl_give isl_union_set *isl_union_set_detect_equalities(
1877 __isl_take isl_union_set *uset);
1878 __isl_give isl_union_map *isl_union_map_detect_equalities(
1879 __isl_take isl_union_map *umap);
1881 Simplify the representation of a set or relation by detecting implicit
1884 =item * Removing redundant constraints
1886 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1887 __isl_take isl_basic_set *bset);
1888 __isl_give isl_set *isl_set_remove_redundancies(
1889 __isl_take isl_set *set);
1890 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1891 __isl_take isl_basic_map *bmap);
1892 __isl_give isl_map *isl_map_remove_redundancies(
1893 __isl_take isl_map *map);
1897 __isl_give isl_basic_set *isl_set_convex_hull(
1898 __isl_take isl_set *set);
1899 __isl_give isl_basic_map *isl_map_convex_hull(
1900 __isl_take isl_map *map);
1902 If the input set or relation has any existentially quantified
1903 variables, then the result of these operations is currently undefined.
1907 __isl_give isl_basic_set *isl_set_simple_hull(
1908 __isl_take isl_set *set);
1909 __isl_give isl_basic_map *isl_map_simple_hull(
1910 __isl_take isl_map *map);
1911 __isl_give isl_union_map *isl_union_map_simple_hull(
1912 __isl_take isl_union_map *umap);
1914 These functions compute a single basic set or relation
1915 that contains the whole input set or relation.
1916 In particular, the output is described by translates
1917 of the constraints describing the basic sets or relations in the input.
1921 (See \autoref{s:simple hull}.)
1927 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1928 __isl_take isl_basic_set *bset);
1929 __isl_give isl_basic_set *isl_set_affine_hull(
1930 __isl_take isl_set *set);
1931 __isl_give isl_union_set *isl_union_set_affine_hull(
1932 __isl_take isl_union_set *uset);
1933 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1934 __isl_take isl_basic_map *bmap);
1935 __isl_give isl_basic_map *isl_map_affine_hull(
1936 __isl_take isl_map *map);
1937 __isl_give isl_union_map *isl_union_map_affine_hull(
1938 __isl_take isl_union_map *umap);
1940 In case of union sets and relations, the affine hull is computed
1943 =item * Polyhedral hull
1945 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1946 __isl_take isl_set *set);
1947 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1948 __isl_take isl_map *map);
1949 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1950 __isl_take isl_union_set *uset);
1951 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1952 __isl_take isl_union_map *umap);
1954 These functions compute a single basic set or relation
1955 not involving any existentially quantified variables
1956 that contains the whole input set or relation.
1957 In case of union sets and relations, the polyhedral hull is computed
1960 =item * Optimization
1962 #include <isl/ilp.h>
1963 enum isl_lp_result isl_basic_set_max(
1964 __isl_keep isl_basic_set *bset,
1965 __isl_keep isl_aff *obj, isl_int *opt)
1966 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1967 __isl_keep isl_aff *obj, isl_int *opt);
1968 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1969 __isl_keep isl_aff *obj, isl_int *opt);
1971 Compute the minimum or maximum of the integer affine expression C<obj>
1972 over the points in C<set>, returning the result in C<opt>.
1973 The return value may be one of C<isl_lp_error>,
1974 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1976 =item * Parametric optimization
1978 __isl_give isl_pw_aff *isl_set_dim_min(
1979 __isl_take isl_set *set, int pos);
1980 __isl_give isl_pw_aff *isl_set_dim_max(
1981 __isl_take isl_set *set, int pos);
1982 __isl_give isl_pw_aff *isl_map_dim_max(
1983 __isl_take isl_map *map, int pos);
1985 Compute the minimum or maximum of the given set or output dimension
1986 as a function of the parameters (and input dimensions), but independently
1987 of the other set or output dimensions.
1988 For lexicographic optimization, see L<"Lexicographic Optimization">.
1992 The following functions compute either the set of (rational) coefficient
1993 values of valid constraints for the given set or the set of (rational)
1994 values satisfying the constraints with coefficients from the given set.
1995 Internally, these two sets of functions perform essentially the
1996 same operations, except that the set of coefficients is assumed to
1997 be a cone, while the set of values may be any polyhedron.
1998 The current implementation is based on the Farkas lemma and
1999 Fourier-Motzkin elimination, but this may change or be made optional
2000 in future. In particular, future implementations may use different
2001 dualization algorithms or skip the elimination step.
2003 __isl_give isl_basic_set *isl_basic_set_coefficients(
2004 __isl_take isl_basic_set *bset);
2005 __isl_give isl_basic_set *isl_set_coefficients(
2006 __isl_take isl_set *set);
2007 __isl_give isl_union_set *isl_union_set_coefficients(
2008 __isl_take isl_union_set *bset);
2009 __isl_give isl_basic_set *isl_basic_set_solutions(
2010 __isl_take isl_basic_set *bset);
2011 __isl_give isl_basic_set *isl_set_solutions(
2012 __isl_take isl_set *set);
2013 __isl_give isl_union_set *isl_union_set_solutions(
2014 __isl_take isl_union_set *bset);
2018 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2020 __isl_give isl_union_map *isl_union_map_power(
2021 __isl_take isl_union_map *umap, int *exact);
2023 Compute a parametric representation for all positive powers I<k> of C<map>.
2024 The result maps I<k> to a nested relation corresponding to the
2025 I<k>th power of C<map>.
2026 The result may be an overapproximation. If the result is known to be exact,
2027 then C<*exact> is set to C<1>.
2029 =item * Transitive closure
2031 __isl_give isl_map *isl_map_transitive_closure(
2032 __isl_take isl_map *map, int *exact);
2033 __isl_give isl_union_map *isl_union_map_transitive_closure(
2034 __isl_take isl_union_map *umap, int *exact);
2036 Compute the transitive closure of C<map>.
2037 The result may be an overapproximation. If the result is known to be exact,
2038 then C<*exact> is set to C<1>.
2040 =item * Reaching path lengths
2042 __isl_give isl_map *isl_map_reaching_path_lengths(
2043 __isl_take isl_map *map, int *exact);
2045 Compute a relation that maps each element in the range of C<map>
2046 to the lengths of all paths composed of edges in C<map> that
2047 end up in the given element.
2048 The result may be an overapproximation. If the result is known to be exact,
2049 then C<*exact> is set to C<1>.
2050 To compute the I<maximal> path length, the resulting relation
2051 should be postprocessed by C<isl_map_lexmax>.
2052 In particular, if the input relation is a dependence relation
2053 (mapping sources to sinks), then the maximal path length corresponds
2054 to the free schedule.
2055 Note, however, that C<isl_map_lexmax> expects the maximum to be
2056 finite, so if the path lengths are unbounded (possibly due to
2057 the overapproximation), then you will get an error message.
2061 __isl_give isl_basic_set *isl_basic_map_wrap(
2062 __isl_take isl_basic_map *bmap);
2063 __isl_give isl_set *isl_map_wrap(
2064 __isl_take isl_map *map);
2065 __isl_give isl_union_set *isl_union_map_wrap(
2066 __isl_take isl_union_map *umap);
2067 __isl_give isl_basic_map *isl_basic_set_unwrap(
2068 __isl_take isl_basic_set *bset);
2069 __isl_give isl_map *isl_set_unwrap(
2070 __isl_take isl_set *set);
2071 __isl_give isl_union_map *isl_union_set_unwrap(
2072 __isl_take isl_union_set *uset);
2076 Remove any internal structure of domain (and range) of the given
2077 set or relation. If there is any such internal structure in the input,
2078 then the name of the space is also removed.
2080 __isl_give isl_basic_set *isl_basic_set_flatten(
2081 __isl_take isl_basic_set *bset);
2082 __isl_give isl_set *isl_set_flatten(
2083 __isl_take isl_set *set);
2084 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2085 __isl_take isl_basic_map *bmap);
2086 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2087 __isl_take isl_basic_map *bmap);
2088 __isl_give isl_map *isl_map_flatten_range(
2089 __isl_take isl_map *map);
2090 __isl_give isl_map *isl_map_flatten_domain(
2091 __isl_take isl_map *map);
2092 __isl_give isl_basic_map *isl_basic_map_flatten(
2093 __isl_take isl_basic_map *bmap);
2094 __isl_give isl_map *isl_map_flatten(
2095 __isl_take isl_map *map);
2097 __isl_give isl_map *isl_set_flatten_map(
2098 __isl_take isl_set *set);
2100 The function above constructs a relation
2101 that maps the input set to a flattened version of the set.
2105 Lift the input set to a space with extra dimensions corresponding
2106 to the existentially quantified variables in the input.
2107 In particular, the result lives in a wrapped map where the domain
2108 is the original space and the range corresponds to the original
2109 existentially quantified variables.
2111 __isl_give isl_basic_set *isl_basic_set_lift(
2112 __isl_take isl_basic_set *bset);
2113 __isl_give isl_set *isl_set_lift(
2114 __isl_take isl_set *set);
2115 __isl_give isl_union_set *isl_union_set_lift(
2116 __isl_take isl_union_set *uset);
2118 Given a local space that contains the existentially quantified
2119 variables of a set, a basic relation that, when applied to
2120 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2121 can be constructed using the following function.
2123 #include <isl/local_space.h>
2124 __isl_give isl_basic_map *isl_local_space_lifting(
2125 __isl_take isl_local_space *ls);
2127 =item * Internal Product
2129 __isl_give isl_basic_map *isl_basic_map_zip(
2130 __isl_take isl_basic_map *bmap);
2131 __isl_give isl_map *isl_map_zip(
2132 __isl_take isl_map *map);
2133 __isl_give isl_union_map *isl_union_map_zip(
2134 __isl_take isl_union_map *umap);
2136 Given a relation with nested relations for domain and range,
2137 interchange the range of the domain with the domain of the range.
2139 =item * Aligning parameters
2141 __isl_give isl_set *isl_set_align_params(
2142 __isl_take isl_set *set,
2143 __isl_take isl_space *model);
2144 __isl_give isl_map *isl_map_align_params(
2145 __isl_take isl_map *map,
2146 __isl_take isl_space *model);
2148 Change the order of the parameters of the given set or relation
2149 such that the first parameters match those of C<model>.
2150 This may involve the introduction of extra parameters.
2151 All parameters need to be named.
2153 =item * Dimension manipulation
2155 __isl_give isl_set *isl_set_add_dims(
2156 __isl_take isl_set *set,
2157 enum isl_dim_type type, unsigned n);
2158 __isl_give isl_map *isl_map_add_dims(
2159 __isl_take isl_map *map,
2160 enum isl_dim_type type, unsigned n);
2161 __isl_give isl_set *isl_set_insert_dims(
2162 __isl_take isl_set *set,
2163 enum isl_dim_type type, unsigned pos, unsigned n);
2164 __isl_give isl_map *isl_map_insert_dims(
2165 __isl_take isl_map *map,
2166 enum isl_dim_type type, unsigned pos, unsigned n);
2167 __isl_give isl_basic_set *isl_basic_set_move_dims(
2168 __isl_take isl_basic_set *bset,
2169 enum isl_dim_type dst_type, unsigned dst_pos,
2170 enum isl_dim_type src_type, unsigned src_pos,
2172 __isl_give isl_basic_map *isl_basic_map_move_dims(
2173 __isl_take isl_basic_map *bmap,
2174 enum isl_dim_type dst_type, unsigned dst_pos,
2175 enum isl_dim_type src_type, unsigned src_pos,
2177 __isl_give isl_set *isl_set_move_dims(
2178 __isl_take isl_set *set,
2179 enum isl_dim_type dst_type, unsigned dst_pos,
2180 enum isl_dim_type src_type, unsigned src_pos,
2182 __isl_give isl_map *isl_map_move_dims(
2183 __isl_take isl_map *map,
2184 enum isl_dim_type dst_type, unsigned dst_pos,
2185 enum isl_dim_type src_type, unsigned src_pos,
2188 It is usually not advisable to directly change the (input or output)
2189 space of a set or a relation as this removes the name and the internal
2190 structure of the space. However, the above functions can be useful
2191 to add new parameters, assuming
2192 C<isl_set_align_params> and C<isl_map_align_params>
2197 =head2 Binary Operations
2199 The two arguments of a binary operation not only need to live
2200 in the same C<isl_ctx>, they currently also need to have
2201 the same (number of) parameters.
2203 =head3 Basic Operations
2207 =item * Intersection
2209 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2210 __isl_take isl_basic_set *bset1,
2211 __isl_take isl_basic_set *bset2);
2212 __isl_give isl_basic_set *isl_basic_set_intersect(
2213 __isl_take isl_basic_set *bset1,
2214 __isl_take isl_basic_set *bset2);
2215 __isl_give isl_set *isl_set_intersect_params(
2216 __isl_take isl_set *set,
2217 __isl_take isl_set *params);
2218 __isl_give isl_set *isl_set_intersect(
2219 __isl_take isl_set *set1,
2220 __isl_take isl_set *set2);
2221 __isl_give isl_union_set *isl_union_set_intersect_params(
2222 __isl_take isl_union_set *uset,
2223 __isl_take isl_set *set);
2224 __isl_give isl_union_map *isl_union_map_intersect_params(
2225 __isl_take isl_union_map *umap,
2226 __isl_take isl_set *set);
2227 __isl_give isl_union_set *isl_union_set_intersect(
2228 __isl_take isl_union_set *uset1,
2229 __isl_take isl_union_set *uset2);
2230 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2231 __isl_take isl_basic_map *bmap,
2232 __isl_take isl_basic_set *bset);
2233 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2234 __isl_take isl_basic_map *bmap,
2235 __isl_take isl_basic_set *bset);
2236 __isl_give isl_basic_map *isl_basic_map_intersect(
2237 __isl_take isl_basic_map *bmap1,
2238 __isl_take isl_basic_map *bmap2);
2239 __isl_give isl_map *isl_map_intersect_params(
2240 __isl_take isl_map *map,
2241 __isl_take isl_set *params);
2242 __isl_give isl_map *isl_map_intersect_domain(
2243 __isl_take isl_map *map,
2244 __isl_take isl_set *set);
2245 __isl_give isl_map *isl_map_intersect_range(
2246 __isl_take isl_map *map,
2247 __isl_take isl_set *set);
2248 __isl_give isl_map *isl_map_intersect(
2249 __isl_take isl_map *map1,
2250 __isl_take isl_map *map2);
2251 __isl_give isl_union_map *isl_union_map_intersect_domain(
2252 __isl_take isl_union_map *umap,
2253 __isl_take isl_union_set *uset);
2254 __isl_give isl_union_map *isl_union_map_intersect_range(
2255 __isl_take isl_union_map *umap,
2256 __isl_take isl_union_set *uset);
2257 __isl_give isl_union_map *isl_union_map_intersect(
2258 __isl_take isl_union_map *umap1,
2259 __isl_take isl_union_map *umap2);
2263 __isl_give isl_set *isl_basic_set_union(
2264 __isl_take isl_basic_set *bset1,
2265 __isl_take isl_basic_set *bset2);
2266 __isl_give isl_map *isl_basic_map_union(
2267 __isl_take isl_basic_map *bmap1,
2268 __isl_take isl_basic_map *bmap2);
2269 __isl_give isl_set *isl_set_union(
2270 __isl_take isl_set *set1,
2271 __isl_take isl_set *set2);
2272 __isl_give isl_map *isl_map_union(
2273 __isl_take isl_map *map1,
2274 __isl_take isl_map *map2);
2275 __isl_give isl_union_set *isl_union_set_union(
2276 __isl_take isl_union_set *uset1,
2277 __isl_take isl_union_set *uset2);
2278 __isl_give isl_union_map *isl_union_map_union(
2279 __isl_take isl_union_map *umap1,
2280 __isl_take isl_union_map *umap2);
2282 =item * Set difference
2284 __isl_give isl_set *isl_set_subtract(
2285 __isl_take isl_set *set1,
2286 __isl_take isl_set *set2);
2287 __isl_give isl_map *isl_map_subtract(
2288 __isl_take isl_map *map1,
2289 __isl_take isl_map *map2);
2290 __isl_give isl_map *isl_map_subtract_domain(
2291 __isl_take isl_map *map,
2292 __isl_take isl_set *dom);
2293 __isl_give isl_map *isl_map_subtract_range(
2294 __isl_take isl_map *map,
2295 __isl_take isl_set *dom);
2296 __isl_give isl_union_set *isl_union_set_subtract(
2297 __isl_take isl_union_set *uset1,
2298 __isl_take isl_union_set *uset2);
2299 __isl_give isl_union_map *isl_union_map_subtract(
2300 __isl_take isl_union_map *umap1,
2301 __isl_take isl_union_map *umap2);
2305 __isl_give isl_basic_set *isl_basic_set_apply(
2306 __isl_take isl_basic_set *bset,
2307 __isl_take isl_basic_map *bmap);
2308 __isl_give isl_set *isl_set_apply(
2309 __isl_take isl_set *set,
2310 __isl_take isl_map *map);
2311 __isl_give isl_union_set *isl_union_set_apply(
2312 __isl_take isl_union_set *uset,
2313 __isl_take isl_union_map *umap);
2314 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2315 __isl_take isl_basic_map *bmap1,
2316 __isl_take isl_basic_map *bmap2);
2317 __isl_give isl_basic_map *isl_basic_map_apply_range(
2318 __isl_take isl_basic_map *bmap1,
2319 __isl_take isl_basic_map *bmap2);
2320 __isl_give isl_map *isl_map_apply_domain(
2321 __isl_take isl_map *map1,
2322 __isl_take isl_map *map2);
2323 __isl_give isl_union_map *isl_union_map_apply_domain(
2324 __isl_take isl_union_map *umap1,
2325 __isl_take isl_union_map *umap2);
2326 __isl_give isl_map *isl_map_apply_range(
2327 __isl_take isl_map *map1,
2328 __isl_take isl_map *map2);
2329 __isl_give isl_union_map *isl_union_map_apply_range(
2330 __isl_take isl_union_map *umap1,
2331 __isl_take isl_union_map *umap2);
2333 =item * Cartesian Product
2335 __isl_give isl_set *isl_set_product(
2336 __isl_take isl_set *set1,
2337 __isl_take isl_set *set2);
2338 __isl_give isl_union_set *isl_union_set_product(
2339 __isl_take isl_union_set *uset1,
2340 __isl_take isl_union_set *uset2);
2341 __isl_give isl_basic_map *isl_basic_map_domain_product(
2342 __isl_take isl_basic_map *bmap1,
2343 __isl_take isl_basic_map *bmap2);
2344 __isl_give isl_basic_map *isl_basic_map_range_product(
2345 __isl_take isl_basic_map *bmap1,
2346 __isl_take isl_basic_map *bmap2);
2347 __isl_give isl_map *isl_map_domain_product(
2348 __isl_take isl_map *map1,
2349 __isl_take isl_map *map2);
2350 __isl_give isl_map *isl_map_range_product(
2351 __isl_take isl_map *map1,
2352 __isl_take isl_map *map2);
2353 __isl_give isl_union_map *isl_union_map_range_product(
2354 __isl_take isl_union_map *umap1,
2355 __isl_take isl_union_map *umap2);
2356 __isl_give isl_map *isl_map_product(
2357 __isl_take isl_map *map1,
2358 __isl_take isl_map *map2);
2359 __isl_give isl_union_map *isl_union_map_product(
2360 __isl_take isl_union_map *umap1,
2361 __isl_take isl_union_map *umap2);
2363 The above functions compute the cross product of the given
2364 sets or relations. The domains and ranges of the results
2365 are wrapped maps between domains and ranges of the inputs.
2366 To obtain a ``flat'' product, use the following functions
2369 __isl_give isl_basic_set *isl_basic_set_flat_product(
2370 __isl_take isl_basic_set *bset1,
2371 __isl_take isl_basic_set *bset2);
2372 __isl_give isl_set *isl_set_flat_product(
2373 __isl_take isl_set *set1,
2374 __isl_take isl_set *set2);
2375 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2376 __isl_take isl_basic_map *bmap1,
2377 __isl_take isl_basic_map *bmap2);
2378 __isl_give isl_map *isl_map_flat_domain_product(
2379 __isl_take isl_map *map1,
2380 __isl_take isl_map *map2);
2381 __isl_give isl_map *isl_map_flat_range_product(
2382 __isl_take isl_map *map1,
2383 __isl_take isl_map *map2);
2384 __isl_give isl_union_map *isl_union_map_flat_range_product(
2385 __isl_take isl_union_map *umap1,
2386 __isl_take isl_union_map *umap2);
2387 __isl_give isl_basic_map *isl_basic_map_flat_product(
2388 __isl_take isl_basic_map *bmap1,
2389 __isl_take isl_basic_map *bmap2);
2390 __isl_give isl_map *isl_map_flat_product(
2391 __isl_take isl_map *map1,
2392 __isl_take isl_map *map2);
2394 =item * Simplification
2396 __isl_give isl_basic_set *isl_basic_set_gist(
2397 __isl_take isl_basic_set *bset,
2398 __isl_take isl_basic_set *context);
2399 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2400 __isl_take isl_set *context);
2401 __isl_give isl_set *isl_set_gist_params(
2402 __isl_take isl_set *set,
2403 __isl_take isl_set *context);
2404 __isl_give isl_union_set *isl_union_set_gist(
2405 __isl_take isl_union_set *uset,
2406 __isl_take isl_union_set *context);
2407 __isl_give isl_union_set *isl_union_set_gist_params(
2408 __isl_take isl_union_set *uset,
2409 __isl_take isl_set *set);
2410 __isl_give isl_basic_map *isl_basic_map_gist(
2411 __isl_take isl_basic_map *bmap,
2412 __isl_take isl_basic_map *context);
2413 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2414 __isl_take isl_map *context);
2415 __isl_give isl_map *isl_map_gist_params(
2416 __isl_take isl_map *map,
2417 __isl_take isl_set *context);
2418 __isl_give isl_map *isl_map_gist_domain(
2419 __isl_take isl_map *map,
2420 __isl_take isl_set *context);
2421 __isl_give isl_map *isl_map_gist_range(
2422 __isl_take isl_map *map,
2423 __isl_take isl_set *context);
2424 __isl_give isl_union_map *isl_union_map_gist(
2425 __isl_take isl_union_map *umap,
2426 __isl_take isl_union_map *context);
2427 __isl_give isl_union_map *isl_union_map_gist_params(
2428 __isl_take isl_union_map *umap,
2429 __isl_take isl_set *set);
2430 __isl_give isl_union_map *isl_union_map_gist_domain(
2431 __isl_take isl_union_map *umap,
2432 __isl_take isl_union_set *uset);
2434 The gist operation returns a set or relation that has the
2435 same intersection with the context as the input set or relation.
2436 Any implicit equality in the intersection is made explicit in the result,
2437 while all inequalities that are redundant with respect to the intersection
2439 In case of union sets and relations, the gist operation is performed
2444 =head3 Lexicographic Optimization
2446 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2447 the following functions
2448 compute a set that contains the lexicographic minimum or maximum
2449 of the elements in C<set> (or C<bset>) for those values of the parameters
2450 that satisfy C<dom>.
2451 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2452 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2454 In other words, the union of the parameter values
2455 for which the result is non-empty and of C<*empty>
2458 __isl_give isl_set *isl_basic_set_partial_lexmin(
2459 __isl_take isl_basic_set *bset,
2460 __isl_take isl_basic_set *dom,
2461 __isl_give isl_set **empty);
2462 __isl_give isl_set *isl_basic_set_partial_lexmax(
2463 __isl_take isl_basic_set *bset,
2464 __isl_take isl_basic_set *dom,
2465 __isl_give isl_set **empty);
2466 __isl_give isl_set *isl_set_partial_lexmin(
2467 __isl_take isl_set *set, __isl_take isl_set *dom,
2468 __isl_give isl_set **empty);
2469 __isl_give isl_set *isl_set_partial_lexmax(
2470 __isl_take isl_set *set, __isl_take isl_set *dom,
2471 __isl_give isl_set **empty);
2473 Given a (basic) set C<set> (or C<bset>), the following functions simply
2474 return a set containing the lexicographic minimum or maximum
2475 of the elements in C<set> (or C<bset>).
2476 In case of union sets, the optimum is computed per space.
2478 __isl_give isl_set *isl_basic_set_lexmin(
2479 __isl_take isl_basic_set *bset);
2480 __isl_give isl_set *isl_basic_set_lexmax(
2481 __isl_take isl_basic_set *bset);
2482 __isl_give isl_set *isl_set_lexmin(
2483 __isl_take isl_set *set);
2484 __isl_give isl_set *isl_set_lexmax(
2485 __isl_take isl_set *set);
2486 __isl_give isl_union_set *isl_union_set_lexmin(
2487 __isl_take isl_union_set *uset);
2488 __isl_give isl_union_set *isl_union_set_lexmax(
2489 __isl_take isl_union_set *uset);
2491 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2492 the following functions
2493 compute a relation that maps each element of C<dom>
2494 to the single lexicographic minimum or maximum
2495 of the elements that are associated to that same
2496 element in C<map> (or C<bmap>).
2497 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2498 that contains the elements in C<dom> that do not map
2499 to any elements in C<map> (or C<bmap>).
2500 In other words, the union of the domain of the result and of C<*empty>
2503 __isl_give isl_map *isl_basic_map_partial_lexmax(
2504 __isl_take isl_basic_map *bmap,
2505 __isl_take isl_basic_set *dom,
2506 __isl_give isl_set **empty);
2507 __isl_give isl_map *isl_basic_map_partial_lexmin(
2508 __isl_take isl_basic_map *bmap,
2509 __isl_take isl_basic_set *dom,
2510 __isl_give isl_set **empty);
2511 __isl_give isl_map *isl_map_partial_lexmax(
2512 __isl_take isl_map *map, __isl_take isl_set *dom,
2513 __isl_give isl_set **empty);
2514 __isl_give isl_map *isl_map_partial_lexmin(
2515 __isl_take isl_map *map, __isl_take isl_set *dom,
2516 __isl_give isl_set **empty);
2518 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2519 return a map mapping each element in the domain of
2520 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2521 of all elements associated to that element.
2522 In case of union relations, the optimum is computed per space.
2524 __isl_give isl_map *isl_basic_map_lexmin(
2525 __isl_take isl_basic_map *bmap);
2526 __isl_give isl_map *isl_basic_map_lexmax(
2527 __isl_take isl_basic_map *bmap);
2528 __isl_give isl_map *isl_map_lexmin(
2529 __isl_take isl_map *map);
2530 __isl_give isl_map *isl_map_lexmax(
2531 __isl_take isl_map *map);
2532 __isl_give isl_union_map *isl_union_map_lexmin(
2533 __isl_take isl_union_map *umap);
2534 __isl_give isl_union_map *isl_union_map_lexmax(
2535 __isl_take isl_union_map *umap);
2537 The following functions return their result in the form of
2538 a piecewise multi-affine expression
2539 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2540 but are otherwise equivalent to the corresponding functions
2541 returning a basic set or relation.
2543 __isl_give isl_pw_multi_aff *
2544 isl_basic_map_lexmin_pw_multi_aff(
2545 __isl_take isl_basic_map *bmap);
2546 __isl_give isl_pw_multi_aff *
2547 isl_basic_set_partial_lexmin_pw_multi_aff(
2548 __isl_take isl_basic_set *bset,
2549 __isl_take isl_basic_set *dom,
2550 __isl_give isl_set **empty);
2551 __isl_give isl_pw_multi_aff *
2552 isl_basic_set_partial_lexmax_pw_multi_aff(
2553 __isl_take isl_basic_set *bset,
2554 __isl_take isl_basic_set *dom,
2555 __isl_give isl_set **empty);
2556 __isl_give isl_pw_multi_aff *
2557 isl_basic_map_partial_lexmin_pw_multi_aff(
2558 __isl_take isl_basic_map *bmap,
2559 __isl_take isl_basic_set *dom,
2560 __isl_give isl_set **empty);
2561 __isl_give isl_pw_multi_aff *
2562 isl_basic_map_partial_lexmax_pw_multi_aff(
2563 __isl_take isl_basic_map *bmap,
2564 __isl_take isl_basic_set *dom,
2565 __isl_give isl_set **empty);
2569 Lists are defined over several element types, including
2570 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2571 Here we take lists of C<isl_set>s as an example.
2572 Lists can be created, copied and freed using the following functions.
2574 #include <isl/list.h>
2575 __isl_give isl_set_list *isl_set_list_from_set(
2576 __isl_take isl_set *el);
2577 __isl_give isl_set_list *isl_set_list_alloc(
2578 isl_ctx *ctx, int n);
2579 __isl_give isl_set_list *isl_set_list_copy(
2580 __isl_keep isl_set_list *list);
2581 __isl_give isl_set_list *isl_set_list_add(
2582 __isl_take isl_set_list *list,
2583 __isl_take isl_set *el);
2584 __isl_give isl_set_list *isl_set_list_concat(
2585 __isl_take isl_set_list *list1,
2586 __isl_take isl_set_list *list2);
2587 void *isl_set_list_free(__isl_take isl_set_list *list);
2589 C<isl_set_list_alloc> creates an empty list with a capacity for
2590 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2593 Lists can be inspected using the following functions.
2595 #include <isl/list.h>
2596 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2597 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2598 __isl_give isl_set *isl_set_list_get_set(
2599 __isl_keep isl_set_list *list, int index);
2600 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2601 int (*fn)(__isl_take isl_set *el, void *user),
2604 Lists can be printed using
2606 #include <isl/list.h>
2607 __isl_give isl_printer *isl_printer_print_set_list(
2608 __isl_take isl_printer *p,
2609 __isl_keep isl_set_list *list);
2613 Matrices can be created, copied and freed using the following functions.
2615 #include <isl/mat.h>
2616 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2617 unsigned n_row, unsigned n_col);
2618 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2619 void isl_mat_free(__isl_take isl_mat *mat);
2621 Note that the elements of a newly created matrix may have arbitrary values.
2622 The elements can be changed and inspected using the following functions.
2624 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2625 int isl_mat_rows(__isl_keep isl_mat *mat);
2626 int isl_mat_cols(__isl_keep isl_mat *mat);
2627 int isl_mat_get_element(__isl_keep isl_mat *mat,
2628 int row, int col, isl_int *v);
2629 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2630 int row, int col, isl_int v);
2631 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2632 int row, int col, int v);
2634 C<isl_mat_get_element> will return a negative value if anything went wrong.
2635 In that case, the value of C<*v> is undefined.
2637 The following function can be used to compute the (right) inverse
2638 of a matrix, i.e., a matrix such that the product of the original
2639 and the inverse (in that order) is a multiple of the identity matrix.
2640 The input matrix is assumed to be of full row-rank.
2642 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2644 The following function can be used to compute the (right) kernel
2645 (or null space) of a matrix, i.e., a matrix such that the product of
2646 the original and the kernel (in that order) is the zero matrix.
2648 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2650 =head2 Piecewise Quasi Affine Expressions
2652 The zero quasi affine expression on a given domain can be created using
2654 __isl_give isl_aff *isl_aff_zero_on_domain(
2655 __isl_take isl_local_space *ls);
2657 Note that the space in which the resulting object lives is a map space
2658 with the given space as domain and a one-dimensional range.
2660 An empty piecewise quasi affine expression (one with no cells)
2661 or a piecewise quasi affine expression with a single cell can
2662 be created using the following functions.
2664 #include <isl/aff.h>
2665 __isl_give isl_pw_aff *isl_pw_aff_empty(
2666 __isl_take isl_space *space);
2667 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2668 __isl_take isl_set *set, __isl_take isl_aff *aff);
2669 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2670 __isl_take isl_aff *aff);
2672 Quasi affine expressions can be copied and freed using
2674 #include <isl/aff.h>
2675 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2676 void *isl_aff_free(__isl_take isl_aff *aff);
2678 __isl_give isl_pw_aff *isl_pw_aff_copy(
2679 __isl_keep isl_pw_aff *pwaff);
2680 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2682 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2683 using the following function. The constraint is required to have
2684 a non-zero coefficient for the specified dimension.
2686 #include <isl/constraint.h>
2687 __isl_give isl_aff *isl_constraint_get_bound(
2688 __isl_keep isl_constraint *constraint,
2689 enum isl_dim_type type, int pos);
2691 The entire affine expression of the constraint can also be extracted
2692 using the following function.
2694 #include <isl/constraint.h>
2695 __isl_give isl_aff *isl_constraint_get_aff(
2696 __isl_keep isl_constraint *constraint);
2698 Conversely, an equality constraint equating
2699 the affine expression to zero or an inequality constraint enforcing
2700 the affine expression to be non-negative, can be constructed using
2702 __isl_give isl_constraint *isl_equality_from_aff(
2703 __isl_take isl_aff *aff);
2704 __isl_give isl_constraint *isl_inequality_from_aff(
2705 __isl_take isl_aff *aff);
2707 The expression can be inspected using
2709 #include <isl/aff.h>
2710 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2711 int isl_aff_dim(__isl_keep isl_aff *aff,
2712 enum isl_dim_type type);
2713 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2714 __isl_keep isl_aff *aff);
2715 __isl_give isl_local_space *isl_aff_get_local_space(
2716 __isl_keep isl_aff *aff);
2717 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2718 enum isl_dim_type type, unsigned pos);
2719 const char *isl_pw_aff_get_dim_name(
2720 __isl_keep isl_pw_aff *pa,
2721 enum isl_dim_type type, unsigned pos);
2722 __isl_give isl_id *isl_pw_aff_get_dim_id(
2723 __isl_keep isl_pw_aff *pa,
2724 enum isl_dim_type type, unsigned pos);
2725 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2727 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2728 enum isl_dim_type type, int pos, isl_int *v);
2729 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2731 __isl_give isl_aff *isl_aff_get_div(
2732 __isl_keep isl_aff *aff, int pos);
2734 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2735 int (*fn)(__isl_take isl_set *set,
2736 __isl_take isl_aff *aff,
2737 void *user), void *user);
2739 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2740 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2742 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2743 enum isl_dim_type type, unsigned first, unsigned n);
2744 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2745 enum isl_dim_type type, unsigned first, unsigned n);
2747 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2748 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2749 enum isl_dim_type type);
2750 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2752 It can be modified using
2754 #include <isl/aff.h>
2755 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2756 __isl_take isl_pw_aff *pwaff,
2757 enum isl_dim_type type, __isl_take isl_id *id);
2758 __isl_give isl_aff *isl_aff_set_dim_name(
2759 __isl_take isl_aff *aff, enum isl_dim_type type,
2760 unsigned pos, const char *s);
2761 __isl_give isl_aff *isl_aff_set_dim_id(
2762 __isl_take isl_aff *aff, enum isl_dim_type type,
2763 unsigned pos, __isl_take isl_id *id);
2764 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2765 __isl_take isl_pw_aff *pma,
2766 enum isl_dim_type type, unsigned pos,
2767 __isl_take isl_id *id);
2768 __isl_give isl_aff *isl_aff_set_constant(
2769 __isl_take isl_aff *aff, isl_int v);
2770 __isl_give isl_aff *isl_aff_set_constant_si(
2771 __isl_take isl_aff *aff, int v);
2772 __isl_give isl_aff *isl_aff_set_coefficient(
2773 __isl_take isl_aff *aff,
2774 enum isl_dim_type type, int pos, isl_int v);
2775 __isl_give isl_aff *isl_aff_set_coefficient_si(
2776 __isl_take isl_aff *aff,
2777 enum isl_dim_type type, int pos, int v);
2778 __isl_give isl_aff *isl_aff_set_denominator(
2779 __isl_take isl_aff *aff, isl_int v);
2781 __isl_give isl_aff *isl_aff_add_constant(
2782 __isl_take isl_aff *aff, isl_int v);
2783 __isl_give isl_aff *isl_aff_add_constant_si(
2784 __isl_take isl_aff *aff, int v);
2785 __isl_give isl_aff *isl_aff_add_coefficient(
2786 __isl_take isl_aff *aff,
2787 enum isl_dim_type type, int pos, isl_int v);
2788 __isl_give isl_aff *isl_aff_add_coefficient_si(
2789 __isl_take isl_aff *aff,
2790 enum isl_dim_type type, int pos, int v);
2792 __isl_give isl_aff *isl_aff_insert_dims(
2793 __isl_take isl_aff *aff,
2794 enum isl_dim_type type, unsigned first, unsigned n);
2795 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2796 __isl_take isl_pw_aff *pwaff,
2797 enum isl_dim_type type, unsigned first, unsigned n);
2798 __isl_give isl_aff *isl_aff_add_dims(
2799 __isl_take isl_aff *aff,
2800 enum isl_dim_type type, unsigned n);
2801 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2802 __isl_take isl_pw_aff *pwaff,
2803 enum isl_dim_type type, unsigned n);
2804 __isl_give isl_aff *isl_aff_drop_dims(
2805 __isl_take isl_aff *aff,
2806 enum isl_dim_type type, unsigned first, unsigned n);
2807 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2808 __isl_take isl_pw_aff *pwaff,
2809 enum isl_dim_type type, unsigned first, unsigned n);
2811 Note that the C<set_constant> and C<set_coefficient> functions
2812 set the I<numerator> of the constant or coefficient, while
2813 C<add_constant> and C<add_coefficient> add an integer value to
2814 the possibly rational constant or coefficient.
2816 To check whether an affine expressions is obviously zero
2817 or obviously equal to some other affine expression, use
2819 #include <isl/aff.h>
2820 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2821 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2822 __isl_keep isl_aff *aff2);
2823 int isl_pw_aff_plain_is_equal(
2824 __isl_keep isl_pw_aff *pwaff1,
2825 __isl_keep isl_pw_aff *pwaff2);
2829 #include <isl/aff.h>
2830 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2831 __isl_take isl_aff *aff2);
2832 __isl_give isl_pw_aff *isl_pw_aff_add(
2833 __isl_take isl_pw_aff *pwaff1,
2834 __isl_take isl_pw_aff *pwaff2);
2835 __isl_give isl_pw_aff *isl_pw_aff_min(
2836 __isl_take isl_pw_aff *pwaff1,
2837 __isl_take isl_pw_aff *pwaff2);
2838 __isl_give isl_pw_aff *isl_pw_aff_max(
2839 __isl_take isl_pw_aff *pwaff1,
2840 __isl_take isl_pw_aff *pwaff2);
2841 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2842 __isl_take isl_aff *aff2);
2843 __isl_give isl_pw_aff *isl_pw_aff_sub(
2844 __isl_take isl_pw_aff *pwaff1,
2845 __isl_take isl_pw_aff *pwaff2);
2846 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2847 __isl_give isl_pw_aff *isl_pw_aff_neg(
2848 __isl_take isl_pw_aff *pwaff);
2849 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2850 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2851 __isl_take isl_pw_aff *pwaff);
2852 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2853 __isl_give isl_pw_aff *isl_pw_aff_floor(
2854 __isl_take isl_pw_aff *pwaff);
2855 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2857 __isl_give isl_pw_aff *isl_pw_aff_mod(
2858 __isl_take isl_pw_aff *pwaff, isl_int mod);
2859 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2861 __isl_give isl_pw_aff *isl_pw_aff_scale(
2862 __isl_take isl_pw_aff *pwaff, isl_int f);
2863 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2865 __isl_give isl_aff *isl_aff_scale_down_ui(
2866 __isl_take isl_aff *aff, unsigned f);
2867 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2868 __isl_take isl_pw_aff *pwaff, isl_int f);
2870 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2871 __isl_take isl_pw_aff_list *list);
2872 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2873 __isl_take isl_pw_aff_list *list);
2875 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2876 __isl_take isl_pw_aff *pwqp);
2878 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2879 __isl_take isl_pw_aff *pwaff,
2880 __isl_take isl_space *model);
2882 __isl_give isl_aff *isl_aff_gist_params(
2883 __isl_take isl_aff *aff,
2884 __isl_take isl_set *context);
2885 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2886 __isl_take isl_set *context);
2887 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
2888 __isl_take isl_pw_aff *pwaff,
2889 __isl_take isl_set *context);
2890 __isl_give isl_pw_aff *isl_pw_aff_gist(
2891 __isl_take isl_pw_aff *pwaff,
2892 __isl_take isl_set *context);
2894 __isl_give isl_set *isl_pw_aff_domain(
2895 __isl_take isl_pw_aff *pwaff);
2896 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2897 __isl_take isl_pw_aff *pa,
2898 __isl_take isl_set *set);
2899 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
2900 __isl_take isl_pw_aff *pa,
2901 __isl_take isl_set *set);
2903 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2904 __isl_take isl_aff *aff2);
2905 __isl_give isl_pw_aff *isl_pw_aff_mul(
2906 __isl_take isl_pw_aff *pwaff1,
2907 __isl_take isl_pw_aff *pwaff2);
2909 When multiplying two affine expressions, at least one of the two needs
2912 #include <isl/aff.h>
2913 __isl_give isl_basic_set *isl_aff_le_basic_set(
2914 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2915 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2916 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2917 __isl_give isl_set *isl_pw_aff_eq_set(
2918 __isl_take isl_pw_aff *pwaff1,
2919 __isl_take isl_pw_aff *pwaff2);
2920 __isl_give isl_set *isl_pw_aff_ne_set(
2921 __isl_take isl_pw_aff *pwaff1,
2922 __isl_take isl_pw_aff *pwaff2);
2923 __isl_give isl_set *isl_pw_aff_le_set(
2924 __isl_take isl_pw_aff *pwaff1,
2925 __isl_take isl_pw_aff *pwaff2);
2926 __isl_give isl_set *isl_pw_aff_lt_set(
2927 __isl_take isl_pw_aff *pwaff1,
2928 __isl_take isl_pw_aff *pwaff2);
2929 __isl_give isl_set *isl_pw_aff_ge_set(
2930 __isl_take isl_pw_aff *pwaff1,
2931 __isl_take isl_pw_aff *pwaff2);
2932 __isl_give isl_set *isl_pw_aff_gt_set(
2933 __isl_take isl_pw_aff *pwaff1,
2934 __isl_take isl_pw_aff *pwaff2);
2936 __isl_give isl_set *isl_pw_aff_list_eq_set(
2937 __isl_take isl_pw_aff_list *list1,
2938 __isl_take isl_pw_aff_list *list2);
2939 __isl_give isl_set *isl_pw_aff_list_ne_set(
2940 __isl_take isl_pw_aff_list *list1,
2941 __isl_take isl_pw_aff_list *list2);
2942 __isl_give isl_set *isl_pw_aff_list_le_set(
2943 __isl_take isl_pw_aff_list *list1,
2944 __isl_take isl_pw_aff_list *list2);
2945 __isl_give isl_set *isl_pw_aff_list_lt_set(
2946 __isl_take isl_pw_aff_list *list1,
2947 __isl_take isl_pw_aff_list *list2);
2948 __isl_give isl_set *isl_pw_aff_list_ge_set(
2949 __isl_take isl_pw_aff_list *list1,
2950 __isl_take isl_pw_aff_list *list2);
2951 __isl_give isl_set *isl_pw_aff_list_gt_set(
2952 __isl_take isl_pw_aff_list *list1,
2953 __isl_take isl_pw_aff_list *list2);
2955 The function C<isl_aff_ge_basic_set> returns a basic set
2956 containing those elements in the shared space
2957 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2958 The function C<isl_aff_ge_set> returns a set
2959 containing those elements in the shared domain
2960 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2961 The functions operating on C<isl_pw_aff_list> apply the corresponding
2962 C<isl_pw_aff> function to each pair of elements in the two lists.
2964 #include <isl/aff.h>
2965 __isl_give isl_set *isl_pw_aff_nonneg_set(
2966 __isl_take isl_pw_aff *pwaff);
2967 __isl_give isl_set *isl_pw_aff_zero_set(
2968 __isl_take isl_pw_aff *pwaff);
2969 __isl_give isl_set *isl_pw_aff_non_zero_set(
2970 __isl_take isl_pw_aff *pwaff);
2972 The function C<isl_pw_aff_nonneg_set> returns a set
2973 containing those elements in the domain
2974 of C<pwaff> where C<pwaff> is non-negative.
2976 #include <isl/aff.h>
2977 __isl_give isl_pw_aff *isl_pw_aff_cond(
2978 __isl_take isl_set *cond,
2979 __isl_take isl_pw_aff *pwaff_true,
2980 __isl_take isl_pw_aff *pwaff_false);
2982 The function C<isl_pw_aff_cond> performs a conditional operator
2983 and returns an expression that is equal to C<pwaff_true>
2984 for elements in C<cond> and equal to C<pwaff_false> for elements
2987 #include <isl/aff.h>
2988 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2989 __isl_take isl_pw_aff *pwaff1,
2990 __isl_take isl_pw_aff *pwaff2);
2991 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2992 __isl_take isl_pw_aff *pwaff1,
2993 __isl_take isl_pw_aff *pwaff2);
2994 __isl_give isl_pw_aff *isl_pw_aff_union_add(
2995 __isl_take isl_pw_aff *pwaff1,
2996 __isl_take isl_pw_aff *pwaff2);
2998 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2999 expression with a domain that is the union of those of C<pwaff1> and
3000 C<pwaff2> and such that on each cell, the quasi-affine expression is
3001 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3002 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3003 associated expression is the defined one.
3005 An expression can be read from input using
3007 #include <isl/aff.h>
3008 __isl_give isl_aff *isl_aff_read_from_str(
3009 isl_ctx *ctx, const char *str);
3010 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3011 isl_ctx *ctx, const char *str);
3013 An expression can be printed using
3015 #include <isl/aff.h>
3016 __isl_give isl_printer *isl_printer_print_aff(
3017 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3019 __isl_give isl_printer *isl_printer_print_pw_aff(
3020 __isl_take isl_printer *p,
3021 __isl_keep isl_pw_aff *pwaff);
3023 =head2 Piecewise Multiple Quasi Affine Expressions
3025 An C<isl_multi_aff> object represents a sequence of
3026 zero or more affine expressions, all defined on the same domain space.
3028 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3031 #include <isl/aff.h>
3032 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3033 __isl_take isl_space *space,
3034 __isl_take isl_aff_list *list);
3036 An empty piecewise multiple quasi affine expression (one with no cells) or
3037 a piecewise multiple quasi affine expression with a single cell can
3038 be created using the following functions.
3040 #include <isl/aff.h>
3041 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3042 __isl_take isl_space *space);
3043 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3044 __isl_take isl_set *set,
3045 __isl_take isl_multi_aff *maff);
3047 A piecewise multiple quasi affine expression can also be initialized
3048 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3049 and the C<isl_map> is single-valued.
3051 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3052 __isl_take isl_set *set);
3053 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3054 __isl_take isl_map *map);
3056 Multiple quasi affine expressions can be copied and freed using
3058 #include <isl/aff.h>
3059 __isl_give isl_multi_aff *isl_multi_aff_copy(
3060 __isl_keep isl_multi_aff *maff);
3061 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3063 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3064 __isl_keep isl_pw_multi_aff *pma);
3065 void *isl_pw_multi_aff_free(
3066 __isl_take isl_pw_multi_aff *pma);
3068 The expression can be inspected using
3070 #include <isl/aff.h>
3071 isl_ctx *isl_multi_aff_get_ctx(
3072 __isl_keep isl_multi_aff *maff);
3073 isl_ctx *isl_pw_multi_aff_get_ctx(
3074 __isl_keep isl_pw_multi_aff *pma);
3075 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3076 enum isl_dim_type type);
3077 unsigned isl_pw_multi_aff_dim(
3078 __isl_keep isl_pw_multi_aff *pma,
3079 enum isl_dim_type type);
3080 __isl_give isl_aff *isl_multi_aff_get_aff(
3081 __isl_keep isl_multi_aff *multi, int pos);
3082 const char *isl_pw_multi_aff_get_dim_name(
3083 __isl_keep isl_pw_multi_aff *pma,
3084 enum isl_dim_type type, unsigned pos);
3085 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3086 __isl_keep isl_pw_multi_aff *pma,
3087 enum isl_dim_type type, unsigned pos);
3088 const char *isl_multi_aff_get_tuple_name(
3089 __isl_keep isl_multi_aff *multi,
3090 enum isl_dim_type type);
3091 const char *isl_pw_multi_aff_get_tuple_name(
3092 __isl_keep isl_pw_multi_aff *pma,
3093 enum isl_dim_type type);
3094 int isl_pw_multi_aff_has_tuple_id(
3095 __isl_keep isl_pw_multi_aff *pma,
3096 enum isl_dim_type type);
3097 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3098 __isl_keep isl_pw_multi_aff *pma,
3099 enum isl_dim_type type);
3101 int isl_pw_multi_aff_foreach_piece(
3102 __isl_keep isl_pw_multi_aff *pma,
3103 int (*fn)(__isl_take isl_set *set,
3104 __isl_take isl_multi_aff *maff,
3105 void *user), void *user);
3107 It can be modified using
3109 #include <isl/aff.h>
3110 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3111 __isl_take isl_multi_aff *maff,
3112 enum isl_dim_type type, unsigned pos, const char *s);
3113 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3114 __isl_take isl_pw_multi_aff *pma,
3115 enum isl_dim_type type, __isl_take isl_id *id);
3117 To check whether two multiple affine expressions are
3118 obviously equal to each other, use
3120 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3121 __isl_keep isl_multi_aff *maff2);
3122 int isl_pw_multi_aff_plain_is_equal(
3123 __isl_keep isl_pw_multi_aff *pma1,
3124 __isl_keep isl_pw_multi_aff *pma2);
3128 #include <isl/aff.h>
3129 __isl_give isl_multi_aff *isl_multi_aff_add(
3130 __isl_take isl_multi_aff *maff1,
3131 __isl_take isl_multi_aff *maff2);
3132 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3133 __isl_take isl_pw_multi_aff *pma1,
3134 __isl_take isl_pw_multi_aff *pma2);
3135 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3136 __isl_take isl_pw_multi_aff *pma1,
3137 __isl_take isl_pw_multi_aff *pma2);
3138 __isl_give isl_multi_aff *isl_multi_aff_scale(
3139 __isl_take isl_multi_aff *maff,
3141 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3142 __isl_take isl_pw_multi_aff *pma,
3143 __isl_take isl_set *set);
3144 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3145 __isl_take isl_pw_multi_aff *pma,
3146 __isl_take isl_set *set);
3147 __isl_give isl_multi_aff *isl_multi_aff_lift(
3148 __isl_take isl_multi_aff *maff,
3149 __isl_give isl_local_space **ls);
3150 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3151 __isl_take isl_multi_aff *maff,
3152 __isl_take isl_set *context);
3153 __isl_give isl_multi_aff *isl_multi_aff_gist(
3154 __isl_take isl_multi_aff *maff,
3155 __isl_take isl_set *context);
3156 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3157 __isl_take isl_pw_multi_aff *pma,
3158 __isl_take isl_set *set);
3159 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3160 __isl_take isl_pw_multi_aff *pma,
3161 __isl_take isl_set *set);
3163 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3164 then it is assigned the local space that lies at the basis of
3165 the lifting applied.
3167 An expression can be read from input using
3169 #include <isl/aff.h>
3170 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3171 isl_ctx *ctx, const char *str);
3172 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3173 isl_ctx *ctx, const char *str);
3175 An expression can be printed using
3177 #include <isl/aff.h>
3178 __isl_give isl_printer *isl_printer_print_multi_aff(
3179 __isl_take isl_printer *p,
3180 __isl_keep isl_multi_aff *maff);
3181 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3182 __isl_take isl_printer *p,
3183 __isl_keep isl_pw_multi_aff *pma);
3187 Points are elements of a set. They can be used to construct
3188 simple sets (boxes) or they can be used to represent the
3189 individual elements of a set.
3190 The zero point (the origin) can be created using
3192 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3194 The coordinates of a point can be inspected, set and changed
3197 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3198 enum isl_dim_type type, int pos, isl_int *v);
3199 __isl_give isl_point *isl_point_set_coordinate(
3200 __isl_take isl_point *pnt,
3201 enum isl_dim_type type, int pos, isl_int v);
3203 __isl_give isl_point *isl_point_add_ui(
3204 __isl_take isl_point *pnt,
3205 enum isl_dim_type type, int pos, unsigned val);
3206 __isl_give isl_point *isl_point_sub_ui(
3207 __isl_take isl_point *pnt,
3208 enum isl_dim_type type, int pos, unsigned val);
3210 Other properties can be obtained using
3212 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3214 Points can be copied or freed using
3216 __isl_give isl_point *isl_point_copy(
3217 __isl_keep isl_point *pnt);
3218 void isl_point_free(__isl_take isl_point *pnt);
3220 A singleton set can be created from a point using
3222 __isl_give isl_basic_set *isl_basic_set_from_point(
3223 __isl_take isl_point *pnt);
3224 __isl_give isl_set *isl_set_from_point(
3225 __isl_take isl_point *pnt);
3227 and a box can be created from two opposite extremal points using
3229 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3230 __isl_take isl_point *pnt1,
3231 __isl_take isl_point *pnt2);
3232 __isl_give isl_set *isl_set_box_from_points(
3233 __isl_take isl_point *pnt1,
3234 __isl_take isl_point *pnt2);
3236 All elements of a B<bounded> (union) set can be enumerated using
3237 the following functions.
3239 int isl_set_foreach_point(__isl_keep isl_set *set,
3240 int (*fn)(__isl_take isl_point *pnt, void *user),
3242 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3243 int (*fn)(__isl_take isl_point *pnt, void *user),
3246 The function C<fn> is called for each integer point in
3247 C<set> with as second argument the last argument of
3248 the C<isl_set_foreach_point> call. The function C<fn>
3249 should return C<0> on success and C<-1> on failure.
3250 In the latter case, C<isl_set_foreach_point> will stop
3251 enumerating and return C<-1> as well.
3252 If the enumeration is performed successfully and to completion,
3253 then C<isl_set_foreach_point> returns C<0>.
3255 To obtain a single point of a (basic) set, use
3257 __isl_give isl_point *isl_basic_set_sample_point(
3258 __isl_take isl_basic_set *bset);
3259 __isl_give isl_point *isl_set_sample_point(
3260 __isl_take isl_set *set);
3262 If C<set> does not contain any (integer) points, then the
3263 resulting point will be ``void'', a property that can be
3266 int isl_point_is_void(__isl_keep isl_point *pnt);
3268 =head2 Piecewise Quasipolynomials
3270 A piecewise quasipolynomial is a particular kind of function that maps
3271 a parametric point to a rational value.
3272 More specifically, a quasipolynomial is a polynomial expression in greatest
3273 integer parts of affine expressions of parameters and variables.
3274 A piecewise quasipolynomial is a subdivision of a given parametric
3275 domain into disjoint cells with a quasipolynomial associated to
3276 each cell. The value of the piecewise quasipolynomial at a given
3277 point is the value of the quasipolynomial associated to the cell
3278 that contains the point. Outside of the union of cells,
3279 the value is assumed to be zero.
3280 For example, the piecewise quasipolynomial
3282 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3284 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3285 A given piecewise quasipolynomial has a fixed domain dimension.
3286 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3287 defined over different domains.
3288 Piecewise quasipolynomials are mainly used by the C<barvinok>
3289 library for representing the number of elements in a parametric set or map.
3290 For example, the piecewise quasipolynomial above represents
3291 the number of points in the map
3293 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3295 =head3 Input and Output
3297 Piecewise quasipolynomials can be read from input using
3299 __isl_give isl_union_pw_qpolynomial *
3300 isl_union_pw_qpolynomial_read_from_str(
3301 isl_ctx *ctx, const char *str);
3303 Quasipolynomials and piecewise quasipolynomials can be printed
3304 using the following functions.
3306 __isl_give isl_printer *isl_printer_print_qpolynomial(
3307 __isl_take isl_printer *p,
3308 __isl_keep isl_qpolynomial *qp);
3310 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3311 __isl_take isl_printer *p,
3312 __isl_keep isl_pw_qpolynomial *pwqp);
3314 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3315 __isl_take isl_printer *p,
3316 __isl_keep isl_union_pw_qpolynomial *upwqp);
3318 The output format of the printer
3319 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3320 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3322 In case of printing in C<ISL_FORMAT_C>, the user may want
3323 to set the names of all dimensions
3325 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3326 __isl_take isl_qpolynomial *qp,
3327 enum isl_dim_type type, unsigned pos,
3329 __isl_give isl_pw_qpolynomial *
3330 isl_pw_qpolynomial_set_dim_name(
3331 __isl_take isl_pw_qpolynomial *pwqp,
3332 enum isl_dim_type type, unsigned pos,
3335 =head3 Creating New (Piecewise) Quasipolynomials
3337 Some simple quasipolynomials can be created using the following functions.
3338 More complicated quasipolynomials can be created by applying
3339 operations such as addition and multiplication
3340 on the resulting quasipolynomials
3342 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3343 __isl_take isl_space *domain);
3344 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3345 __isl_take isl_space *domain);
3346 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3347 __isl_take isl_space *domain);
3348 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3349 __isl_take isl_space *domain);
3350 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3351 __isl_take isl_space *domain);
3352 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3353 __isl_take isl_space *domain,
3354 const isl_int n, const isl_int d);
3355 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3356 __isl_take isl_space *domain,
3357 enum isl_dim_type type, unsigned pos);
3358 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3359 __isl_take isl_aff *aff);
3361 Note that the space in which a quasipolynomial lives is a map space
3362 with a one-dimensional range. The C<domain> argument in some of
3363 the functions above corresponds to the domain of this map space.
3365 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3366 with a single cell can be created using the following functions.
3367 Multiple of these single cell piecewise quasipolynomials can
3368 be combined to create more complicated piecewise quasipolynomials.
3370 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3371 __isl_take isl_space *space);
3372 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3373 __isl_take isl_set *set,
3374 __isl_take isl_qpolynomial *qp);
3375 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3376 __isl_take isl_qpolynomial *qp);
3377 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3378 __isl_take isl_pw_aff *pwaff);
3380 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3381 __isl_take isl_space *space);
3382 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3383 __isl_take isl_pw_qpolynomial *pwqp);
3384 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3385 __isl_take isl_union_pw_qpolynomial *upwqp,
3386 __isl_take isl_pw_qpolynomial *pwqp);
3388 Quasipolynomials can be copied and freed again using the following
3391 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3392 __isl_keep isl_qpolynomial *qp);
3393 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3395 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3396 __isl_keep isl_pw_qpolynomial *pwqp);
3397 void *isl_pw_qpolynomial_free(
3398 __isl_take isl_pw_qpolynomial *pwqp);
3400 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3401 __isl_keep isl_union_pw_qpolynomial *upwqp);
3402 void isl_union_pw_qpolynomial_free(
3403 __isl_take isl_union_pw_qpolynomial *upwqp);
3405 =head3 Inspecting (Piecewise) Quasipolynomials
3407 To iterate over all piecewise quasipolynomials in a union
3408 piecewise quasipolynomial, use the following function
3410 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3411 __isl_keep isl_union_pw_qpolynomial *upwqp,
3412 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3415 To extract the piecewise quasipolynomial in a given space from a union, use
3417 __isl_give isl_pw_qpolynomial *
3418 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3419 __isl_keep isl_union_pw_qpolynomial *upwqp,
3420 __isl_take isl_space *space);
3422 To iterate over the cells in a piecewise quasipolynomial,
3423 use either of the following two functions
3425 int isl_pw_qpolynomial_foreach_piece(
3426 __isl_keep isl_pw_qpolynomial *pwqp,
3427 int (*fn)(__isl_take isl_set *set,
3428 __isl_take isl_qpolynomial *qp,
3429 void *user), void *user);
3430 int isl_pw_qpolynomial_foreach_lifted_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);
3436 As usual, the function C<fn> should return C<0> on success
3437 and C<-1> on failure. The difference between
3438 C<isl_pw_qpolynomial_foreach_piece> and
3439 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3440 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3441 compute unique representations for all existentially quantified
3442 variables and then turn these existentially quantified variables
3443 into extra set variables, adapting the associated quasipolynomial
3444 accordingly. This means that the C<set> passed to C<fn>
3445 will not have any existentially quantified variables, but that
3446 the dimensions of the sets may be different for different
3447 invocations of C<fn>.
3449 To iterate over all terms in a quasipolynomial,
3452 int isl_qpolynomial_foreach_term(
3453 __isl_keep isl_qpolynomial *qp,
3454 int (*fn)(__isl_take isl_term *term,
3455 void *user), void *user);
3457 The terms themselves can be inspected and freed using
3460 unsigned isl_term_dim(__isl_keep isl_term *term,
3461 enum isl_dim_type type);
3462 void isl_term_get_num(__isl_keep isl_term *term,
3464 void isl_term_get_den(__isl_keep isl_term *term,
3466 int isl_term_get_exp(__isl_keep isl_term *term,
3467 enum isl_dim_type type, unsigned pos);
3468 __isl_give isl_aff *isl_term_get_div(
3469 __isl_keep isl_term *term, unsigned pos);
3470 void isl_term_free(__isl_take isl_term *term);
3472 Each term is a product of parameters, set variables and
3473 integer divisions. The function C<isl_term_get_exp>
3474 returns the exponent of a given dimensions in the given term.
3475 The C<isl_int>s in the arguments of C<isl_term_get_num>
3476 and C<isl_term_get_den> need to have been initialized
3477 using C<isl_int_init> before calling these functions.
3479 =head3 Properties of (Piecewise) Quasipolynomials
3481 To check whether a quasipolynomial is actually a constant,
3482 use the following function.
3484 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3485 isl_int *n, isl_int *d);
3487 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3488 then the numerator and denominator of the constant
3489 are returned in C<*n> and C<*d>, respectively.
3491 To check whether two union piecewise quasipolynomials are
3492 obviously equal, use
3494 int isl_union_pw_qpolynomial_plain_is_equal(
3495 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3496 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3498 =head3 Operations on (Piecewise) Quasipolynomials
3500 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3501 __isl_take isl_qpolynomial *qp, isl_int v);
3502 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3503 __isl_take isl_qpolynomial *qp);
3504 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3505 __isl_take isl_qpolynomial *qp1,
3506 __isl_take isl_qpolynomial *qp2);
3507 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3508 __isl_take isl_qpolynomial *qp1,
3509 __isl_take isl_qpolynomial *qp2);
3510 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3511 __isl_take isl_qpolynomial *qp1,
3512 __isl_take isl_qpolynomial *qp2);
3513 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3514 __isl_take isl_qpolynomial *qp, unsigned exponent);
3516 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3517 __isl_take isl_pw_qpolynomial *pwqp1,
3518 __isl_take isl_pw_qpolynomial *pwqp2);
3519 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3520 __isl_take isl_pw_qpolynomial *pwqp1,
3521 __isl_take isl_pw_qpolynomial *pwqp2);
3522 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3523 __isl_take isl_pw_qpolynomial *pwqp1,
3524 __isl_take isl_pw_qpolynomial *pwqp2);
3525 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3526 __isl_take isl_pw_qpolynomial *pwqp);
3527 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3528 __isl_take isl_pw_qpolynomial *pwqp1,
3529 __isl_take isl_pw_qpolynomial *pwqp2);
3530 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3531 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3533 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3534 __isl_take isl_union_pw_qpolynomial *upwqp1,
3535 __isl_take isl_union_pw_qpolynomial *upwqp2);
3536 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3537 __isl_take isl_union_pw_qpolynomial *upwqp1,
3538 __isl_take isl_union_pw_qpolynomial *upwqp2);
3539 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3540 __isl_take isl_union_pw_qpolynomial *upwqp1,
3541 __isl_take isl_union_pw_qpolynomial *upwqp2);
3543 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3544 __isl_take isl_pw_qpolynomial *pwqp,
3545 __isl_take isl_point *pnt);
3547 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3548 __isl_take isl_union_pw_qpolynomial *upwqp,
3549 __isl_take isl_point *pnt);
3551 __isl_give isl_set *isl_pw_qpolynomial_domain(
3552 __isl_take isl_pw_qpolynomial *pwqp);
3553 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3554 __isl_take isl_pw_qpolynomial *pwpq,
3555 __isl_take isl_set *set);
3556 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3557 __isl_take isl_pw_qpolynomial *pwpq,
3558 __isl_take isl_set *set);
3560 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3561 __isl_take isl_union_pw_qpolynomial *upwqp);
3562 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3563 __isl_take isl_union_pw_qpolynomial *upwpq,
3564 __isl_take isl_union_set *uset);
3565 __isl_give isl_union_pw_qpolynomial *
3566 isl_union_pw_qpolynomial_intersect_params(
3567 __isl_take isl_union_pw_qpolynomial *upwpq,
3568 __isl_take isl_set *set);
3570 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3571 __isl_take isl_qpolynomial *qp,
3572 __isl_take isl_space *model);
3574 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3575 __isl_take isl_qpolynomial *qp);
3576 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3577 __isl_take isl_pw_qpolynomial *pwqp);
3579 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3580 __isl_take isl_union_pw_qpolynomial *upwqp);
3582 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3583 __isl_take isl_qpolynomial *qp,
3584 __isl_take isl_set *context);
3585 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3586 __isl_take isl_qpolynomial *qp,
3587 __isl_take isl_set *context);
3589 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3590 __isl_take isl_pw_qpolynomial *pwqp,
3591 __isl_take isl_set *context);
3592 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3593 __isl_take isl_pw_qpolynomial *pwqp,
3594 __isl_take isl_set *context);
3596 __isl_give isl_union_pw_qpolynomial *
3597 isl_union_pw_qpolynomial_gist_params(
3598 __isl_take isl_union_pw_qpolynomial *upwqp,
3599 __isl_take isl_set *context);
3600 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3601 __isl_take isl_union_pw_qpolynomial *upwqp,
3602 __isl_take isl_union_set *context);
3604 The gist operation applies the gist operation to each of
3605 the cells in the domain of the input piecewise quasipolynomial.
3606 The context is also exploited
3607 to simplify the quasipolynomials associated to each cell.
3609 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3610 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3611 __isl_give isl_union_pw_qpolynomial *
3612 isl_union_pw_qpolynomial_to_polynomial(
3613 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3615 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3616 the polynomial will be an overapproximation. If C<sign> is negative,
3617 it will be an underapproximation. If C<sign> is zero, the approximation
3618 will lie somewhere in between.
3620 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3622 A piecewise quasipolynomial reduction is a piecewise
3623 reduction (or fold) of quasipolynomials.
3624 In particular, the reduction can be maximum or a minimum.
3625 The objects are mainly used to represent the result of
3626 an upper or lower bound on a quasipolynomial over its domain,
3627 i.e., as the result of the following function.
3629 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3630 __isl_take isl_pw_qpolynomial *pwqp,
3631 enum isl_fold type, int *tight);
3633 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3634 __isl_take isl_union_pw_qpolynomial *upwqp,
3635 enum isl_fold type, int *tight);
3637 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3638 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3639 is the returned bound is known be tight, i.e., for each value
3640 of the parameters there is at least
3641 one element in the domain that reaches the bound.
3642 If the domain of C<pwqp> is not wrapping, then the bound is computed
3643 over all elements in that domain and the result has a purely parametric
3644 domain. If the domain of C<pwqp> is wrapping, then the bound is
3645 computed over the range of the wrapped relation. The domain of the
3646 wrapped relation becomes the domain of the result.
3648 A (piecewise) quasipolynomial reduction can be copied or freed using the
3649 following functions.
3651 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3652 __isl_keep isl_qpolynomial_fold *fold);
3653 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3654 __isl_keep isl_pw_qpolynomial_fold *pwf);
3655 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3656 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3657 void isl_qpolynomial_fold_free(
3658 __isl_take isl_qpolynomial_fold *fold);
3659 void *isl_pw_qpolynomial_fold_free(
3660 __isl_take isl_pw_qpolynomial_fold *pwf);
3661 void isl_union_pw_qpolynomial_fold_free(
3662 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3664 =head3 Printing Piecewise Quasipolynomial Reductions
3666 Piecewise quasipolynomial reductions can be printed
3667 using the following function.
3669 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3670 __isl_take isl_printer *p,
3671 __isl_keep isl_pw_qpolynomial_fold *pwf);
3672 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3673 __isl_take isl_printer *p,
3674 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3676 For C<isl_printer_print_pw_qpolynomial_fold>,
3677 output format of the printer
3678 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3679 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3680 output format of the printer
3681 needs to be set to C<ISL_FORMAT_ISL>.
3682 In case of printing in C<ISL_FORMAT_C>, the user may want
3683 to set the names of all dimensions
3685 __isl_give isl_pw_qpolynomial_fold *
3686 isl_pw_qpolynomial_fold_set_dim_name(
3687 __isl_take isl_pw_qpolynomial_fold *pwf,
3688 enum isl_dim_type type, unsigned pos,
3691 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3693 To iterate over all piecewise quasipolynomial reductions in a union
3694 piecewise quasipolynomial reduction, use the following function
3696 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3697 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3698 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3699 void *user), void *user);
3701 To iterate over the cells in a piecewise quasipolynomial reduction,
3702 use either of the following two functions
3704 int isl_pw_qpolynomial_fold_foreach_piece(
3705 __isl_keep isl_pw_qpolynomial_fold *pwf,
3706 int (*fn)(__isl_take isl_set *set,
3707 __isl_take isl_qpolynomial_fold *fold,
3708 void *user), void *user);
3709 int isl_pw_qpolynomial_fold_foreach_lifted_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);
3715 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3716 of the difference between these two functions.
3718 To iterate over all quasipolynomials in a reduction, use
3720 int isl_qpolynomial_fold_foreach_qpolynomial(
3721 __isl_keep isl_qpolynomial_fold *fold,
3722 int (*fn)(__isl_take isl_qpolynomial *qp,
3723 void *user), void *user);
3725 =head3 Properties of Piecewise Quasipolynomial Reductions
3727 To check whether two union piecewise quasipolynomial reductions are
3728 obviously equal, use
3730 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3731 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3732 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3734 =head3 Operations on Piecewise Quasipolynomial Reductions
3736 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3737 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3739 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3740 __isl_take isl_pw_qpolynomial_fold *pwf1,
3741 __isl_take isl_pw_qpolynomial_fold *pwf2);
3743 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3744 __isl_take isl_pw_qpolynomial_fold *pwf1,
3745 __isl_take isl_pw_qpolynomial_fold *pwf2);
3747 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3748 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3749 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3751 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3752 __isl_take isl_pw_qpolynomial_fold *pwf,
3753 __isl_take isl_point *pnt);
3755 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3756 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3757 __isl_take isl_point *pnt);
3759 __isl_give isl_pw_qpolynomial_fold *
3760 sl_pw_qpolynomial_fold_intersect_params(
3761 __isl_take isl_pw_qpolynomial_fold *pwf,
3762 __isl_take isl_set *set);
3764 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3765 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3766 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3767 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3768 __isl_take isl_union_set *uset);
3769 __isl_give isl_union_pw_qpolynomial_fold *
3770 isl_union_pw_qpolynomial_fold_intersect_params(
3771 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3772 __isl_take isl_set *set);
3774 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3775 __isl_take isl_pw_qpolynomial_fold *pwf);
3777 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3778 __isl_take isl_pw_qpolynomial_fold *pwf);
3780 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3781 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3783 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
3784 __isl_take isl_qpolynomial_fold *fold,
3785 __isl_take isl_set *context);
3786 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
3787 __isl_take isl_qpolynomial_fold *fold,
3788 __isl_take isl_set *context);
3790 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3791 __isl_take isl_pw_qpolynomial_fold *pwf,
3792 __isl_take isl_set *context);
3793 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
3794 __isl_take isl_pw_qpolynomial_fold *pwf,
3795 __isl_take isl_set *context);
3797 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3798 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3799 __isl_take isl_union_set *context);
3800 __isl_give isl_union_pw_qpolynomial_fold *
3801 isl_union_pw_qpolynomial_fold_gist_params(
3802 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3803 __isl_take isl_set *context);
3805 The gist operation applies the gist operation to each of
3806 the cells in the domain of the input piecewise quasipolynomial reduction.
3807 In future, the operation will also exploit the context
3808 to simplify the quasipolynomial reductions associated to each cell.
3810 __isl_give isl_pw_qpolynomial_fold *
3811 isl_set_apply_pw_qpolynomial_fold(
3812 __isl_take isl_set *set,
3813 __isl_take isl_pw_qpolynomial_fold *pwf,
3815 __isl_give isl_pw_qpolynomial_fold *
3816 isl_map_apply_pw_qpolynomial_fold(
3817 __isl_take isl_map *map,
3818 __isl_take isl_pw_qpolynomial_fold *pwf,
3820 __isl_give isl_union_pw_qpolynomial_fold *
3821 isl_union_set_apply_union_pw_qpolynomial_fold(
3822 __isl_take isl_union_set *uset,
3823 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3825 __isl_give isl_union_pw_qpolynomial_fold *
3826 isl_union_map_apply_union_pw_qpolynomial_fold(
3827 __isl_take isl_union_map *umap,
3828 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3831 The functions taking a map
3832 compose the given map with the given piecewise quasipolynomial reduction.
3833 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3834 over all elements in the intersection of the range of the map
3835 and the domain of the piecewise quasipolynomial reduction
3836 as a function of an element in the domain of the map.
3837 The functions taking a set compute a bound over all elements in the
3838 intersection of the set and the domain of the
3839 piecewise quasipolynomial reduction.
3841 =head2 Dependence Analysis
3843 C<isl> contains specialized functionality for performing
3844 array dataflow analysis. That is, given a I<sink> access relation
3845 and a collection of possible I<source> access relations,
3846 C<isl> can compute relations that describe
3847 for each iteration of the sink access, which iteration
3848 of which of the source access relations was the last
3849 to access the same data element before the given iteration
3851 The resulting dependence relations map source iterations
3852 to the corresponding sink iterations.
3853 To compute standard flow dependences, the sink should be
3854 a read, while the sources should be writes.
3855 If any of the source accesses are marked as being I<may>
3856 accesses, then there will be a dependence from the last
3857 I<must> access B<and> from any I<may> access that follows
3858 this last I<must> access.
3859 In particular, if I<all> sources are I<may> accesses,
3860 then memory based dependence analysis is performed.
3861 If, on the other hand, all sources are I<must> accesses,
3862 then value based dependence analysis is performed.
3864 #include <isl/flow.h>
3866 typedef int (*isl_access_level_before)(void *first, void *second);
3868 __isl_give isl_access_info *isl_access_info_alloc(
3869 __isl_take isl_map *sink,
3870 void *sink_user, isl_access_level_before fn,
3872 __isl_give isl_access_info *isl_access_info_add_source(
3873 __isl_take isl_access_info *acc,
3874 __isl_take isl_map *source, int must,
3876 void isl_access_info_free(__isl_take isl_access_info *acc);
3878 __isl_give isl_flow *isl_access_info_compute_flow(
3879 __isl_take isl_access_info *acc);
3881 int isl_flow_foreach(__isl_keep isl_flow *deps,
3882 int (*fn)(__isl_take isl_map *dep, int must,
3883 void *dep_user, void *user),
3885 __isl_give isl_map *isl_flow_get_no_source(
3886 __isl_keep isl_flow *deps, int must);
3887 void isl_flow_free(__isl_take isl_flow *deps);
3889 The function C<isl_access_info_compute_flow> performs the actual
3890 dependence analysis. The other functions are used to construct
3891 the input for this function or to read off the output.
3893 The input is collected in an C<isl_access_info>, which can
3894 be created through a call to C<isl_access_info_alloc>.
3895 The arguments to this functions are the sink access relation
3896 C<sink>, a token C<sink_user> used to identify the sink
3897 access to the user, a callback function for specifying the
3898 relative order of source and sink accesses, and the number
3899 of source access relations that will be added.
3900 The callback function has type C<int (*)(void *first, void *second)>.
3901 The function is called with two user supplied tokens identifying
3902 either a source or the sink and it should return the shared nesting
3903 level and the relative order of the two accesses.
3904 In particular, let I<n> be the number of loops shared by
3905 the two accesses. If C<first> precedes C<second> textually,
3906 then the function should return I<2 * n + 1>; otherwise,
3907 it should return I<2 * n>.
3908 The sources can be added to the C<isl_access_info> by performing
3909 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3910 C<must> indicates whether the source is a I<must> access
3911 or a I<may> access. Note that a multi-valued access relation
3912 should only be marked I<must> if every iteration in the domain
3913 of the relation accesses I<all> elements in its image.
3914 The C<source_user> token is again used to identify
3915 the source access. The range of the source access relation
3916 C<source> should have the same dimension as the range
3917 of the sink access relation.
3918 The C<isl_access_info_free> function should usually not be
3919 called explicitly, because it is called implicitly by
3920 C<isl_access_info_compute_flow>.
3922 The result of the dependence analysis is collected in an
3923 C<isl_flow>. There may be elements of
3924 the sink access for which no preceding source access could be
3925 found or for which all preceding sources are I<may> accesses.
3926 The relations containing these elements can be obtained through
3927 calls to C<isl_flow_get_no_source>, the first with C<must> set
3928 and the second with C<must> unset.
3929 In the case of standard flow dependence analysis,
3930 with the sink a read and the sources I<must> writes,
3931 the first relation corresponds to the reads from uninitialized
3932 array elements and the second relation is empty.
3933 The actual flow dependences can be extracted using
3934 C<isl_flow_foreach>. This function will call the user-specified
3935 callback function C<fn> for each B<non-empty> dependence between
3936 a source and the sink. The callback function is called
3937 with four arguments, the actual flow dependence relation
3938 mapping source iterations to sink iterations, a boolean that
3939 indicates whether it is a I<must> or I<may> dependence, a token
3940 identifying the source and an additional C<void *> with value
3941 equal to the third argument of the C<isl_flow_foreach> call.
3942 A dependence is marked I<must> if it originates from a I<must>
3943 source and if it is not followed by any I<may> sources.
3945 After finishing with an C<isl_flow>, the user should call
3946 C<isl_flow_free> to free all associated memory.
3948 A higher-level interface to dependence analysis is provided
3949 by the following function.
3951 #include <isl/flow.h>
3953 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3954 __isl_take isl_union_map *must_source,
3955 __isl_take isl_union_map *may_source,
3956 __isl_take isl_union_map *schedule,
3957 __isl_give isl_union_map **must_dep,
3958 __isl_give isl_union_map **may_dep,
3959 __isl_give isl_union_map **must_no_source,
3960 __isl_give isl_union_map **may_no_source);
3962 The arrays are identified by the tuple names of the ranges
3963 of the accesses. The iteration domains by the tuple names
3964 of the domains of the accesses and of the schedule.
3965 The relative order of the iteration domains is given by the
3966 schedule. The relations returned through C<must_no_source>
3967 and C<may_no_source> are subsets of C<sink>.
3968 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3969 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3970 any of the other arguments is treated as an error.
3974 B<The functionality described in this section is fairly new
3975 and may be subject to change.>
3977 The following function can be used to compute a schedule
3978 for a union of domains. The generated schedule respects
3979 all C<validity> dependences. That is, all dependence distances
3980 over these dependences in the scheduled space are lexicographically
3981 positive. The generated schedule schedule also tries to minimize
3982 the dependence distances over C<proximity> dependences.
3983 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3984 for groups of domains where the dependence distances have only
3985 non-negative values.
3986 The algorithm used to construct the schedule is similar to that
3989 #include <isl/schedule.h>
3990 __isl_give isl_schedule *isl_union_set_compute_schedule(
3991 __isl_take isl_union_set *domain,
3992 __isl_take isl_union_map *validity,
3993 __isl_take isl_union_map *proximity);
3994 void *isl_schedule_free(__isl_take isl_schedule *sched);
3996 A mapping from the domains to the scheduled space can be obtained
3997 from an C<isl_schedule> using the following function.
3999 __isl_give isl_union_map *isl_schedule_get_map(
4000 __isl_keep isl_schedule *sched);
4002 A representation of the schedule can be printed using
4004 __isl_give isl_printer *isl_printer_print_schedule(
4005 __isl_take isl_printer *p,
4006 __isl_keep isl_schedule *schedule);
4008 A representation of the schedule as a forest of bands can be obtained
4009 using the following function.
4011 __isl_give isl_band_list *isl_schedule_get_band_forest(
4012 __isl_keep isl_schedule *schedule);
4014 The list can be manipulated as explained in L<"Lists">.
4015 The bands inside the list can be copied and freed using the following
4018 #include <isl/band.h>
4019 __isl_give isl_band *isl_band_copy(
4020 __isl_keep isl_band *band);
4021 void *isl_band_free(__isl_take isl_band *band);
4023 Each band contains zero or more scheduling dimensions.
4024 These are referred to as the members of the band.
4025 The section of the schedule that corresponds to the band is
4026 referred to as the partial schedule of the band.
4027 For those nodes that participate in a band, the outer scheduling
4028 dimensions form the prefix schedule, while the inner scheduling
4029 dimensions form the suffix schedule.
4030 That is, if we take a cut of the band forest, then the union of
4031 the concatenations of the prefix, partial and suffix schedules of
4032 each band in the cut is equal to the entire schedule (modulo
4033 some possible padding at the end with zero scheduling dimensions).
4034 The properties of a band can be inspected using the following functions.
4036 #include <isl/band.h>
4037 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4039 int isl_band_has_children(__isl_keep isl_band *band);
4040 __isl_give isl_band_list *isl_band_get_children(
4041 __isl_keep isl_band *band);
4043 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4044 __isl_keep isl_band *band);
4045 __isl_give isl_union_map *isl_band_get_partial_schedule(
4046 __isl_keep isl_band *band);
4047 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4048 __isl_keep isl_band *band);
4050 int isl_band_n_member(__isl_keep isl_band *band);
4051 int isl_band_member_is_zero_distance(
4052 __isl_keep isl_band *band, int pos);
4054 Note that a scheduling dimension is considered to be ``zero
4055 distance'' if it does not carry any proximity dependences
4057 That is, if the dependence distances of the proximity
4058 dependences are all zero in that direction (for fixed
4059 iterations of outer bands).
4061 A representation of the band can be printed using
4063 #include <isl/band.h>
4064 __isl_give isl_printer *isl_printer_print_band(
4065 __isl_take isl_printer *p,
4066 __isl_keep isl_band *band);
4068 =head2 Parametric Vertex Enumeration
4070 The parametric vertex enumeration described in this section
4071 is mainly intended to be used internally and by the C<barvinok>
4074 #include <isl/vertices.h>
4075 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4076 __isl_keep isl_basic_set *bset);
4078 The function C<isl_basic_set_compute_vertices> performs the
4079 actual computation of the parametric vertices and the chamber
4080 decomposition and store the result in an C<isl_vertices> object.
4081 This information can be queried by either iterating over all
4082 the vertices or iterating over all the chambers or cells
4083 and then iterating over all vertices that are active on the chamber.
4085 int isl_vertices_foreach_vertex(
4086 __isl_keep isl_vertices *vertices,
4087 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4090 int isl_vertices_foreach_cell(
4091 __isl_keep isl_vertices *vertices,
4092 int (*fn)(__isl_take isl_cell *cell, void *user),
4094 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4095 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4098 Other operations that can be performed on an C<isl_vertices> object are
4101 isl_ctx *isl_vertices_get_ctx(
4102 __isl_keep isl_vertices *vertices);
4103 int isl_vertices_get_n_vertices(
4104 __isl_keep isl_vertices *vertices);
4105 void isl_vertices_free(__isl_take isl_vertices *vertices);
4107 Vertices can be inspected and destroyed using the following functions.
4109 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4110 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4111 __isl_give isl_basic_set *isl_vertex_get_domain(
4112 __isl_keep isl_vertex *vertex);
4113 __isl_give isl_basic_set *isl_vertex_get_expr(
4114 __isl_keep isl_vertex *vertex);
4115 void isl_vertex_free(__isl_take isl_vertex *vertex);
4117 C<isl_vertex_get_expr> returns a singleton parametric set describing
4118 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4120 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4121 B<rational> basic sets, so they should mainly be used for inspection
4122 and should not be mixed with integer sets.
4124 Chambers can be inspected and destroyed using the following functions.
4126 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4127 __isl_give isl_basic_set *isl_cell_get_domain(
4128 __isl_keep isl_cell *cell);
4129 void isl_cell_free(__isl_take isl_cell *cell);
4133 Although C<isl> is mainly meant to be used as a library,
4134 it also contains some basic applications that use some
4135 of the functionality of C<isl>.
4136 The input may be specified in either the L<isl format>
4137 or the L<PolyLib format>.
4139 =head2 C<isl_polyhedron_sample>
4141 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4142 an integer element of the polyhedron, if there is any.
4143 The first column in the output is the denominator and is always
4144 equal to 1. If the polyhedron contains no integer points,
4145 then a vector of length zero is printed.
4149 C<isl_pip> takes the same input as the C<example> program
4150 from the C<piplib> distribution, i.e., a set of constraints
4151 on the parameters, a line containing only -1 and finally a set
4152 of constraints on a parametric polyhedron.
4153 The coefficients of the parameters appear in the last columns
4154 (but before the final constant column).
4155 The output is the lexicographic minimum of the parametric polyhedron.
4156 As C<isl> currently does not have its own output format, the output
4157 is just a dump of the internal state.
4159 =head2 C<isl_polyhedron_minimize>
4161 C<isl_polyhedron_minimize> computes the minimum of some linear
4162 or affine objective function over the integer points in a polyhedron.
4163 If an affine objective function
4164 is given, then the constant should appear in the last column.
4166 =head2 C<isl_polytope_scan>
4168 Given a polytope, C<isl_polytope_scan> prints
4169 all integer points in the polytope.