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>.
102 =item * The C<isl_dim> type has been renamed to C<isl_space>
103 along with the associated functions.
104 Some of the old names have been kept for backward compatibility,
105 but they will be removed in the future.
107 =item * Spaces of maps, sets and parameter domains are now
108 treated differently. The distinction between map spaces and set spaces
109 has always been made on a conceptual level, but proper use of such spaces
110 was never checked. Furthermore, up until isl-0.07 there was no way
111 of explicitly creating a parameter space. These can now be created
112 directly using C<isl_space_params_alloc> or from other spaces using
115 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
116 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
117 objects live is now a map space
118 instead of a set space. This means, for example, that the dimensions
119 of the domain of an C<isl_aff> are now considered to be of type
120 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
121 added to obtain the domain space. Some of the constructors still
122 take a domain space and have therefore been renamed.
124 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
125 now take an C<isl_local_space> instead of an C<isl_space>.
126 An C<isl_local_space> can be created from an C<isl_space>
127 using C<isl_local_space_from_space>.
129 =item * The C<isl_div> type has been removed. Functions that used
130 to return an C<isl_div> now return an C<isl_aff>.
131 Note that the space of an C<isl_aff> is that of relation.
132 When replacing a call to C<isl_div_get_coefficient> by a call to
133 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
134 to be replaced by C<isl_dim_in>.
135 A call to C<isl_aff_from_div> can be replaced by a call
137 A call to C<isl_qpolynomial_div(div)> call be replaced by
140 isl_qpolynomial_from_aff(isl_aff_floor(div))
142 The function C<isl_constraint_div> has also been renamed
143 to C<isl_constraint_get_div>.
145 =item * The C<nparam> argument has been removed from
146 C<isl_map_read_from_str> and similar functions.
147 When reading input in the original PolyLib format,
148 the result will have no parameters.
149 If parameters are expected, the caller may want to perform
150 dimension manipulation on the result.
156 The source of C<isl> can be obtained either as a tarball
157 or from the git repository. Both are available from
158 L<http://freshmeat.net/projects/isl/>.
159 The installation process depends on how you obtained
162 =head2 Installation from the git repository
166 =item 1 Clone or update the repository
168 The first time the source is obtained, you need to clone
171 git clone git://repo.or.cz/isl.git
173 To obtain updates, you need to pull in the latest changes
177 =item 2 Generate C<configure>
183 After performing the above steps, continue
184 with the L<Common installation instructions>.
186 =head2 Common installation instructions
190 =item 1 Obtain C<GMP>
192 Building C<isl> requires C<GMP>, including its headers files.
193 Your distribution may not provide these header files by default
194 and you may need to install a package called C<gmp-devel> or something
195 similar. Alternatively, C<GMP> can be built from
196 source, available from L<http://gmplib.org/>.
200 C<isl> uses the standard C<autoconf> C<configure> script.
205 optionally followed by some configure options.
206 A complete list of options can be obtained by running
210 Below we discuss some of the more common options.
212 C<isl> can optionally use C<piplib>, but no
213 C<piplib> functionality is currently used by default.
214 The C<--with-piplib> option can
215 be used to specify which C<piplib>
216 library to use, either an installed version (C<system>),
217 an externally built version (C<build>)
218 or no version (C<no>). The option C<build> is mostly useful
219 in C<configure> scripts of larger projects that bundle both C<isl>
226 Installation prefix for C<isl>
228 =item C<--with-gmp-prefix>
230 Installation prefix for C<GMP> (architecture-independent files).
232 =item C<--with-gmp-exec-prefix>
234 Installation prefix for C<GMP> (architecture-dependent files).
236 =item C<--with-piplib>
238 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
240 =item C<--with-piplib-prefix>
242 Installation prefix for C<system> C<piplib> (architecture-independent files).
244 =item C<--with-piplib-exec-prefix>
246 Installation prefix for C<system> C<piplib> (architecture-dependent files).
248 =item C<--with-piplib-builddir>
250 Location where C<build> C<piplib> was built.
258 =item 4 Install (optional)
266 =head2 Initialization
268 All manipulations of integer sets and relations occur within
269 the context of an C<isl_ctx>.
270 A given C<isl_ctx> can only be used within a single thread.
271 All arguments of a function are required to have been allocated
272 within the same context.
273 There are currently no functions available for moving an object
274 from one C<isl_ctx> to another C<isl_ctx>. This means that
275 there is currently no way of safely moving an object from one
276 thread to another, unless the whole C<isl_ctx> is moved.
278 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
279 freed using C<isl_ctx_free>.
280 All objects allocated within an C<isl_ctx> should be freed
281 before the C<isl_ctx> itself is freed.
283 isl_ctx *isl_ctx_alloc();
284 void isl_ctx_free(isl_ctx *ctx);
288 All operations on integers, mainly the coefficients
289 of the constraints describing the sets and relations,
290 are performed in exact integer arithmetic using C<GMP>.
291 However, to allow future versions of C<isl> to optionally
292 support fixed integer arithmetic, all calls to C<GMP>
293 are wrapped inside C<isl> specific macros.
294 The basic type is C<isl_int> and the operations below
295 are available on this type.
296 The meanings of these operations are essentially the same
297 as their C<GMP> C<mpz_> counterparts.
298 As always with C<GMP> types, C<isl_int>s need to be
299 initialized with C<isl_int_init> before they can be used
300 and they need to be released with C<isl_int_clear>
302 The user should not assume that an C<isl_int> is represented
303 as a C<mpz_t>, but should instead explicitly convert between
304 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
305 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
309 =item isl_int_init(i)
311 =item isl_int_clear(i)
313 =item isl_int_set(r,i)
315 =item isl_int_set_si(r,i)
317 =item isl_int_set_gmp(r,g)
319 =item isl_int_get_gmp(i,g)
321 =item isl_int_abs(r,i)
323 =item isl_int_neg(r,i)
325 =item isl_int_swap(i,j)
327 =item isl_int_swap_or_set(i,j)
329 =item isl_int_add_ui(r,i,j)
331 =item isl_int_sub_ui(r,i,j)
333 =item isl_int_add(r,i,j)
335 =item isl_int_sub(r,i,j)
337 =item isl_int_mul(r,i,j)
339 =item isl_int_mul_ui(r,i,j)
341 =item isl_int_addmul(r,i,j)
343 =item isl_int_submul(r,i,j)
345 =item isl_int_gcd(r,i,j)
347 =item isl_int_lcm(r,i,j)
349 =item isl_int_divexact(r,i,j)
351 =item isl_int_cdiv_q(r,i,j)
353 =item isl_int_fdiv_q(r,i,j)
355 =item isl_int_fdiv_r(r,i,j)
357 =item isl_int_fdiv_q_ui(r,i,j)
359 =item isl_int_read(r,s)
361 =item isl_int_print(out,i,width)
365 =item isl_int_cmp(i,j)
367 =item isl_int_cmp_si(i,si)
369 =item isl_int_eq(i,j)
371 =item isl_int_ne(i,j)
373 =item isl_int_lt(i,j)
375 =item isl_int_le(i,j)
377 =item isl_int_gt(i,j)
379 =item isl_int_ge(i,j)
381 =item isl_int_abs_eq(i,j)
383 =item isl_int_abs_ne(i,j)
385 =item isl_int_abs_lt(i,j)
387 =item isl_int_abs_gt(i,j)
389 =item isl_int_abs_ge(i,j)
391 =item isl_int_is_zero(i)
393 =item isl_int_is_one(i)
395 =item isl_int_is_negone(i)
397 =item isl_int_is_pos(i)
399 =item isl_int_is_neg(i)
401 =item isl_int_is_nonpos(i)
403 =item isl_int_is_nonneg(i)
405 =item isl_int_is_divisible_by(i,j)
409 =head2 Sets and Relations
411 C<isl> uses six types of objects for representing sets and relations,
412 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
413 C<isl_union_set> and C<isl_union_map>.
414 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
415 can be described as a conjunction of affine constraints, while
416 C<isl_set> and C<isl_map> represent unions of
417 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
418 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
419 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
420 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
421 where spaces are considered different if they have a different number
422 of dimensions and/or different names (see L<"Spaces">).
423 The difference between sets and relations (maps) is that sets have
424 one set of variables, while relations have two sets of variables,
425 input variables and output variables.
427 =head2 Memory Management
429 Since a high-level operation on sets and/or relations usually involves
430 several substeps and since the user is usually not interested in
431 the intermediate results, most functions that return a new object
432 will also release all the objects passed as arguments.
433 If the user still wants to use one or more of these arguments
434 after the function call, she should pass along a copy of the
435 object rather than the object itself.
436 The user is then responsible for making sure that the original
437 object gets used somewhere else or is explicitly freed.
439 The arguments and return values of all documented functions are
440 annotated to make clear which arguments are released and which
441 arguments are preserved. In particular, the following annotations
448 C<__isl_give> means that a new object is returned.
449 The user should make sure that the returned pointer is
450 used exactly once as a value for an C<__isl_take> argument.
451 In between, it can be used as a value for as many
452 C<__isl_keep> arguments as the user likes.
453 There is one exception, and that is the case where the
454 pointer returned is C<NULL>. Is this case, the user
455 is free to use it as an C<__isl_take> argument or not.
459 C<__isl_take> means that the object the argument points to
460 is taken over by the function and may no longer be used
461 by the user as an argument to any other function.
462 The pointer value must be one returned by a function
463 returning an C<__isl_give> pointer.
464 If the user passes in a C<NULL> value, then this will
465 be treated as an error in the sense that the function will
466 not perform its usual operation. However, it will still
467 make sure that all the other C<__isl_take> arguments
472 C<__isl_keep> means that the function will only use the object
473 temporarily. After the function has finished, the user
474 can still use it as an argument to other functions.
475 A C<NULL> value will be treated in the same way as
476 a C<NULL> value for an C<__isl_take> argument.
482 Identifiers are used to identify both individual dimensions
483 and tuples of dimensions. They consist of a name and an optional
484 pointer. Identifiers with the same name but different pointer values
485 are considered to be distinct.
486 Identifiers can be constructed, copied, freed, inspected and printed
487 using the following functions.
490 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
491 __isl_keep const char *name, void *user);
492 __isl_give isl_id *isl_id_copy(isl_id *id);
493 void *isl_id_free(__isl_take isl_id *id);
495 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
496 void *isl_id_get_user(__isl_keep isl_id *id);
497 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
499 __isl_give isl_printer *isl_printer_print_id(
500 __isl_take isl_printer *p, __isl_keep isl_id *id);
502 Note that C<isl_id_get_name> returns a pointer to some internal
503 data structure, so the result can only be used while the
504 corresponding C<isl_id> is alive.
508 Whenever a new set or relation is created from scratch,
509 the space in which it lives needs to be specified using an C<isl_space>.
511 #include <isl/space.h>
512 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
513 unsigned nparam, unsigned n_in, unsigned n_out);
514 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
516 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
517 unsigned nparam, unsigned dim);
518 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
519 void isl_space_free(__isl_take isl_space *space);
520 unsigned isl_space_dim(__isl_keep isl_space *space,
521 enum isl_dim_type type);
523 The space used for creating a parameter domain
524 needs to be created using C<isl_space_params_alloc>.
525 For other sets, the space
526 needs to be created using C<isl_space_set_alloc>, while
527 for a relation, the space
528 needs to be created using C<isl_space_alloc>.
529 C<isl_space_dim> can be used
530 to find out the number of dimensions of each type in
531 a space, where type may be
532 C<isl_dim_param>, C<isl_dim_in> (only for relations),
533 C<isl_dim_out> (only for relations), C<isl_dim_set>
534 (only for sets) or C<isl_dim_all>.
536 To check whether a given space is that of a set or a map
537 or whether it is a parameter space, use these functions:
539 #include <isl/space.h>
540 int isl_space_is_params(__isl_keep isl_space *space);
541 int isl_space_is_set(__isl_keep isl_space *space);
543 It is often useful to create objects that live in the
544 same space as some other object. This can be accomplished
545 by creating the new objects
546 (see L<Creating New Sets and Relations> or
547 L<Creating New (Piecewise) Quasipolynomials>) based on the space
548 of the original object.
551 __isl_give isl_space *isl_basic_set_get_space(
552 __isl_keep isl_basic_set *bset);
553 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
555 #include <isl/union_set.h>
556 __isl_give isl_space *isl_union_set_get_space(
557 __isl_keep isl_union_set *uset);
560 __isl_give isl_space *isl_basic_map_get_space(
561 __isl_keep isl_basic_map *bmap);
562 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
564 #include <isl/union_map.h>
565 __isl_give isl_space *isl_union_map_get_space(
566 __isl_keep isl_union_map *umap);
568 #include <isl/constraint.h>
569 __isl_give isl_space *isl_constraint_get_space(
570 __isl_keep isl_constraint *constraint);
572 #include <isl/polynomial.h>
573 __isl_give isl_space *isl_qpolynomial_get_domain_space(
574 __isl_keep isl_qpolynomial *qp);
575 __isl_give isl_space *isl_qpolynomial_get_space(
576 __isl_keep isl_qpolynomial *qp);
577 __isl_give isl_space *isl_qpolynomial_fold_get_space(
578 __isl_keep isl_qpolynomial_fold *fold);
579 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
580 __isl_keep isl_pw_qpolynomial *pwqp);
581 __isl_give isl_space *isl_pw_qpolynomial_get_space(
582 __isl_keep isl_pw_qpolynomial *pwqp);
583 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
584 __isl_keep isl_pw_qpolynomial_fold *pwf);
585 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
586 __isl_keep isl_pw_qpolynomial_fold *pwf);
587 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
588 __isl_keep isl_union_pw_qpolynomial *upwqp);
589 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
590 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
593 __isl_give isl_space *isl_aff_get_domain_space(
594 __isl_keep isl_aff *aff);
595 __isl_give isl_space *isl_aff_get_space(
596 __isl_keep isl_aff *aff);
597 __isl_give isl_space *isl_pw_aff_get_domain_space(
598 __isl_keep isl_pw_aff *pwaff);
599 __isl_give isl_space *isl_pw_aff_get_space(
600 __isl_keep isl_pw_aff *pwaff);
602 #include <isl/point.h>
603 __isl_give isl_space *isl_point_get_space(
604 __isl_keep isl_point *pnt);
606 The identifiers or names of the individual dimensions may be set or read off
607 using the following functions.
609 #include <isl/space.h>
610 __isl_give isl_space *isl_space_set_dim_id(
611 __isl_take isl_space *space,
612 enum isl_dim_type type, unsigned pos,
613 __isl_take isl_id *id);
614 int isl_space_has_dim_id(__isl_keep isl_space *space,
615 enum isl_dim_type type, unsigned pos);
616 __isl_give isl_id *isl_space_get_dim_id(
617 __isl_keep isl_space *space,
618 enum isl_dim_type type, unsigned pos);
619 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
620 enum isl_dim_type type, unsigned pos,
621 __isl_keep const char *name);
622 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
623 enum isl_dim_type type, unsigned pos);
625 Note that C<isl_space_get_name> returns a pointer to some internal
626 data structure, so the result can only be used while the
627 corresponding C<isl_space> is alive.
628 Also note that every function that operates on two sets or relations
629 requires that both arguments have the same parameters. This also
630 means that if one of the arguments has named parameters, then the
631 other needs to have named parameters too and the names need to match.
632 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
633 arguments may have different parameters (as long as they are named),
634 in which case the result will have as parameters the union of the parameters of
637 Given the identifier or name of a dimension (typically a parameter),
638 its position can be obtained from the following function.
640 #include <isl/space.h>
641 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
642 enum isl_dim_type type, __isl_keep isl_id *id);
643 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
644 enum isl_dim_type type, const char *name);
646 The identifiers or names of entire spaces may be set or read off
647 using the following functions.
649 #include <isl/space.h>
650 __isl_give isl_space *isl_space_set_tuple_id(
651 __isl_take isl_space *space,
652 enum isl_dim_type type, __isl_take isl_id *id);
653 __isl_give isl_space *isl_space_reset_tuple_id(
654 __isl_take isl_space *space, enum isl_dim_type type);
655 int isl_space_has_tuple_id(__isl_keep isl_space *space,
656 enum isl_dim_type type);
657 __isl_give isl_id *isl_space_get_tuple_id(
658 __isl_keep isl_space *space, enum isl_dim_type type);
659 __isl_give isl_space *isl_space_set_tuple_name(
660 __isl_take isl_space *space,
661 enum isl_dim_type type, const char *s);
662 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
663 enum isl_dim_type type);
665 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
666 or C<isl_dim_set>. As with C<isl_space_get_name>,
667 the C<isl_space_get_tuple_name> function returns a pointer to some internal
669 Binary operations require the corresponding spaces of their arguments
670 to have the same name.
672 Spaces can be nested. In particular, the domain of a set or
673 the domain or range of a relation can be a nested relation.
674 The following functions can be used to construct and deconstruct
677 #include <isl/space.h>
678 int isl_space_is_wrapping(__isl_keep isl_space *space);
679 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
680 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
682 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
683 be the space of a set, while that of
684 C<isl_space_wrap> should be the space of a relation.
685 Conversely, the output of C<isl_space_unwrap> is the space
686 of a relation, while that of C<isl_space_wrap> is the space of a set.
688 Spaces can be created from other spaces
689 using the following functions.
691 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
692 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
693 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
694 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
695 __isl_give isl_space *isl_space_params(
696 __isl_take isl_space *space);
697 __isl_give isl_space *isl_space_set_from_params(
698 __isl_take isl_space *space);
699 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
700 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
701 __isl_take isl_space *right);
702 __isl_give isl_space *isl_space_align_params(
703 __isl_take isl_space *space1, __isl_take isl_space *space2)
704 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
705 enum isl_dim_type type, unsigned pos, unsigned n);
706 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
707 enum isl_dim_type type, unsigned n);
708 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
709 enum isl_dim_type type, unsigned first, unsigned n);
710 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
711 enum isl_dim_type dst_type, unsigned dst_pos,
712 enum isl_dim_type src_type, unsigned src_pos,
714 __isl_give isl_space *isl_space_map_from_set(
715 __isl_take isl_space *space);
716 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
718 Note that if dimensions are added or removed from a space, then
719 the name and the internal structure are lost.
723 A local space is essentially a space with
724 zero or more existentially quantified variables.
725 The local space of a basic set or relation can be obtained
726 using the following functions.
729 __isl_give isl_local_space *isl_basic_set_get_local_space(
730 __isl_keep isl_basic_set *bset);
733 __isl_give isl_local_space *isl_basic_map_get_local_space(
734 __isl_keep isl_basic_map *bmap);
736 A new local space can be created from a space using
738 #include <isl/local_space.h>
739 __isl_give isl_local_space *isl_local_space_from_space(
740 __isl_take isl_space *space);
742 They can be inspected, modified, copied and freed using the following functions.
744 #include <isl/local_space.h>
745 isl_ctx *isl_local_space_get_ctx(
746 __isl_keep isl_local_space *ls);
747 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
748 int isl_local_space_dim(__isl_keep isl_local_space *ls,
749 enum isl_dim_type type);
750 const char *isl_local_space_get_dim_name(
751 __isl_keep isl_local_space *ls,
752 enum isl_dim_type type, unsigned pos);
753 __isl_give isl_local_space *isl_local_space_set_dim_name(
754 __isl_take isl_local_space *ls,
755 enum isl_dim_type type, unsigned pos, const char *s);
756 __isl_give isl_local_space *isl_local_space_set_dim_id(
757 __isl_take isl_local_space *ls,
758 enum isl_dim_type type, unsigned pos,
759 __isl_take isl_id *id);
760 __isl_give isl_space *isl_local_space_get_space(
761 __isl_keep isl_local_space *ls);
762 __isl_give isl_aff *isl_local_space_get_div(
763 __isl_keep isl_local_space *ls, int pos);
764 __isl_give isl_local_space *isl_local_space_copy(
765 __isl_keep isl_local_space *ls);
766 void *isl_local_space_free(__isl_take isl_local_space *ls);
768 Two local spaces can be compared using
770 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
771 __isl_keep isl_local_space *ls2);
773 Local spaces can be created from other local spaces
774 using the following functions.
776 __isl_give isl_local_space *isl_local_space_domain(
777 __isl_take isl_local_space *ls);
778 __isl_give isl_local_space *isl_local_space_from_domain(
779 __isl_take isl_local_space *ls);
780 __isl_give isl_local_space *isl_local_space_add_dims(
781 __isl_take isl_local_space *ls,
782 enum isl_dim_type type, unsigned n);
783 __isl_give isl_local_space *isl_local_space_insert_dims(
784 __isl_take isl_local_space *ls,
785 enum isl_dim_type type, unsigned first, unsigned n);
786 __isl_give isl_local_space *isl_local_space_drop_dims(
787 __isl_take isl_local_space *ls,
788 enum isl_dim_type type, unsigned first, unsigned n);
790 =head2 Input and Output
792 C<isl> supports its own input/output format, which is similar
793 to the C<Omega> format, but also supports the C<PolyLib> format
798 The C<isl> format is similar to that of C<Omega>, but has a different
799 syntax for describing the parameters and allows for the definition
800 of an existentially quantified variable as the integer division
801 of an affine expression.
802 For example, the set of integers C<i> between C<0> and C<n>
803 such that C<i % 10 <= 6> can be described as
805 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
808 A set or relation can have several disjuncts, separated
809 by the keyword C<or>. Each disjunct is either a conjunction
810 of constraints or a projection (C<exists>) of a conjunction
811 of constraints. The constraints are separated by the keyword
814 =head3 C<PolyLib> format
816 If the represented set is a union, then the first line
817 contains a single number representing the number of disjuncts.
818 Otherwise, a line containing the number C<1> is optional.
820 Each disjunct is represented by a matrix of constraints.
821 The first line contains two numbers representing
822 the number of rows and columns,
823 where the number of rows is equal to the number of constraints
824 and the number of columns is equal to two plus the number of variables.
825 The following lines contain the actual rows of the constraint matrix.
826 In each row, the first column indicates whether the constraint
827 is an equality (C<0>) or inequality (C<1>). The final column
828 corresponds to the constant term.
830 If the set is parametric, then the coefficients of the parameters
831 appear in the last columns before the constant column.
832 The coefficients of any existentially quantified variables appear
833 between those of the set variables and those of the parameters.
835 =head3 Extended C<PolyLib> format
837 The extended C<PolyLib> format is nearly identical to the
838 C<PolyLib> format. The only difference is that the line
839 containing the number of rows and columns of a constraint matrix
840 also contains four additional numbers:
841 the number of output dimensions, the number of input dimensions,
842 the number of local dimensions (i.e., the number of existentially
843 quantified variables) and the number of parameters.
844 For sets, the number of ``output'' dimensions is equal
845 to the number of set dimensions, while the number of ``input''
851 __isl_give isl_basic_set *isl_basic_set_read_from_file(
852 isl_ctx *ctx, FILE *input);
853 __isl_give isl_basic_set *isl_basic_set_read_from_str(
854 isl_ctx *ctx, const char *str);
855 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
857 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
861 __isl_give isl_basic_map *isl_basic_map_read_from_file(
862 isl_ctx *ctx, FILE *input);
863 __isl_give isl_basic_map *isl_basic_map_read_from_str(
864 isl_ctx *ctx, const char *str);
865 __isl_give isl_map *isl_map_read_from_file(
866 isl_ctx *ctx, FILE *input);
867 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
870 #include <isl/union_set.h>
871 __isl_give isl_union_set *isl_union_set_read_from_file(
872 isl_ctx *ctx, FILE *input);
873 __isl_give isl_union_set *isl_union_set_read_from_str(
874 isl_ctx *ctx, const char *str);
876 #include <isl/union_map.h>
877 __isl_give isl_union_map *isl_union_map_read_from_file(
878 isl_ctx *ctx, FILE *input);
879 __isl_give isl_union_map *isl_union_map_read_from_str(
880 isl_ctx *ctx, const char *str);
882 The input format is autodetected and may be either the C<PolyLib> format
883 or the C<isl> format.
887 Before anything can be printed, an C<isl_printer> needs to
890 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
892 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
893 void isl_printer_free(__isl_take isl_printer *printer);
894 __isl_give char *isl_printer_get_str(
895 __isl_keep isl_printer *printer);
897 The behavior of the printer can be modified in various ways
899 __isl_give isl_printer *isl_printer_set_output_format(
900 __isl_take isl_printer *p, int output_format);
901 __isl_give isl_printer *isl_printer_set_indent(
902 __isl_take isl_printer *p, int indent);
903 __isl_give isl_printer *isl_printer_indent(
904 __isl_take isl_printer *p, int indent);
905 __isl_give isl_printer *isl_printer_set_prefix(
906 __isl_take isl_printer *p, const char *prefix);
907 __isl_give isl_printer *isl_printer_set_suffix(
908 __isl_take isl_printer *p, const char *suffix);
910 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
911 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
912 and defaults to C<ISL_FORMAT_ISL>.
913 Each line in the output is indented by C<indent> (set by
914 C<isl_printer_set_indent>) spaces
915 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
916 In the C<PolyLib> format output,
917 the coefficients of the existentially quantified variables
918 appear between those of the set variables and those
920 The function C<isl_printer_indent> increases the indentation
921 by the specified amount (which may be negative).
923 To actually print something, use
926 __isl_give isl_printer *isl_printer_print_basic_set(
927 __isl_take isl_printer *printer,
928 __isl_keep isl_basic_set *bset);
929 __isl_give isl_printer *isl_printer_print_set(
930 __isl_take isl_printer *printer,
931 __isl_keep isl_set *set);
934 __isl_give isl_printer *isl_printer_print_basic_map(
935 __isl_take isl_printer *printer,
936 __isl_keep isl_basic_map *bmap);
937 __isl_give isl_printer *isl_printer_print_map(
938 __isl_take isl_printer *printer,
939 __isl_keep isl_map *map);
941 #include <isl/union_set.h>
942 __isl_give isl_printer *isl_printer_print_union_set(
943 __isl_take isl_printer *p,
944 __isl_keep isl_union_set *uset);
946 #include <isl/union_map.h>
947 __isl_give isl_printer *isl_printer_print_union_map(
948 __isl_take isl_printer *p,
949 __isl_keep isl_union_map *umap);
951 When called on a file printer, the following function flushes
952 the file. When called on a string printer, the buffer is cleared.
954 __isl_give isl_printer *isl_printer_flush(
955 __isl_take isl_printer *p);
957 =head2 Creating New Sets and Relations
959 C<isl> has functions for creating some standard sets and relations.
963 =item * Empty sets and relations
965 __isl_give isl_basic_set *isl_basic_set_empty(
966 __isl_take isl_space *space);
967 __isl_give isl_basic_map *isl_basic_map_empty(
968 __isl_take isl_space *space);
969 __isl_give isl_set *isl_set_empty(
970 __isl_take isl_space *space);
971 __isl_give isl_map *isl_map_empty(
972 __isl_take isl_space *space);
973 __isl_give isl_union_set *isl_union_set_empty(
974 __isl_take isl_space *space);
975 __isl_give isl_union_map *isl_union_map_empty(
976 __isl_take isl_space *space);
978 For C<isl_union_set>s and C<isl_union_map>s, the space
979 is only used to specify the parameters.
981 =item * Universe sets and relations
983 __isl_give isl_basic_set *isl_basic_set_universe(
984 __isl_take isl_space *space);
985 __isl_give isl_basic_map *isl_basic_map_universe(
986 __isl_take isl_space *space);
987 __isl_give isl_set *isl_set_universe(
988 __isl_take isl_space *space);
989 __isl_give isl_map *isl_map_universe(
990 __isl_take isl_space *space);
991 __isl_give isl_union_set *isl_union_set_universe(
992 __isl_take isl_union_set *uset);
993 __isl_give isl_union_map *isl_union_map_universe(
994 __isl_take isl_union_map *umap);
996 The sets and relations constructed by the functions above
997 contain all integer values, while those constructed by the
998 functions below only contain non-negative values.
1000 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1001 __isl_take isl_space *space);
1002 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1003 __isl_take isl_space *space);
1004 __isl_give isl_set *isl_set_nat_universe(
1005 __isl_take isl_space *space);
1006 __isl_give isl_map *isl_map_nat_universe(
1007 __isl_take isl_space *space);
1009 =item * Identity relations
1011 __isl_give isl_basic_map *isl_basic_map_identity(
1012 __isl_take isl_space *space);
1013 __isl_give isl_map *isl_map_identity(
1014 __isl_take isl_space *space);
1016 The number of input and output dimensions in C<space> needs
1019 =item * Lexicographic order
1021 __isl_give isl_map *isl_map_lex_lt(
1022 __isl_take isl_space *set_space);
1023 __isl_give isl_map *isl_map_lex_le(
1024 __isl_take isl_space *set_space);
1025 __isl_give isl_map *isl_map_lex_gt(
1026 __isl_take isl_space *set_space);
1027 __isl_give isl_map *isl_map_lex_ge(
1028 __isl_take isl_space *set_space);
1029 __isl_give isl_map *isl_map_lex_lt_first(
1030 __isl_take isl_space *space, unsigned n);
1031 __isl_give isl_map *isl_map_lex_le_first(
1032 __isl_take isl_space *space, unsigned n);
1033 __isl_give isl_map *isl_map_lex_gt_first(
1034 __isl_take isl_space *space, unsigned n);
1035 __isl_give isl_map *isl_map_lex_ge_first(
1036 __isl_take isl_space *space, unsigned n);
1038 The first four functions take a space for a B<set>
1039 and return relations that express that the elements in the domain
1040 are lexicographically less
1041 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1042 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1043 than the elements in the range.
1044 The last four functions take a space for a map
1045 and return relations that express that the first C<n> dimensions
1046 in the domain are lexicographically less
1047 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1048 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1049 than the first C<n> dimensions in the range.
1053 A basic set or relation can be converted to a set or relation
1054 using the following functions.
1056 __isl_give isl_set *isl_set_from_basic_set(
1057 __isl_take isl_basic_set *bset);
1058 __isl_give isl_map *isl_map_from_basic_map(
1059 __isl_take isl_basic_map *bmap);
1061 Sets and relations can be converted to union sets and relations
1062 using the following functions.
1064 __isl_give isl_union_map *isl_union_map_from_map(
1065 __isl_take isl_map *map);
1066 __isl_give isl_union_set *isl_union_set_from_set(
1067 __isl_take isl_set *set);
1069 The inverse conversions below can only be used if the input
1070 union set or relation is known to contain elements in exactly one
1073 __isl_give isl_set *isl_set_from_union_set(
1074 __isl_take isl_union_set *uset);
1075 __isl_give isl_map *isl_map_from_union_map(
1076 __isl_take isl_union_map *umap);
1078 A zero-dimensional set can be constructed on a given parameter domain
1079 using the following function.
1081 __isl_give isl_set *isl_set_from_params(
1082 __isl_take isl_set *set);
1084 Sets and relations can be copied and freed again using the following
1087 __isl_give isl_basic_set *isl_basic_set_copy(
1088 __isl_keep isl_basic_set *bset);
1089 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1090 __isl_give isl_union_set *isl_union_set_copy(
1091 __isl_keep isl_union_set *uset);
1092 __isl_give isl_basic_map *isl_basic_map_copy(
1093 __isl_keep isl_basic_map *bmap);
1094 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1095 __isl_give isl_union_map *isl_union_map_copy(
1096 __isl_keep isl_union_map *umap);
1097 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1098 void isl_set_free(__isl_take isl_set *set);
1099 void *isl_union_set_free(__isl_take isl_union_set *uset);
1100 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1101 void isl_map_free(__isl_take isl_map *map);
1102 void *isl_union_map_free(__isl_take isl_union_map *umap);
1104 Other sets and relations can be constructed by starting
1105 from a universe set or relation, adding equality and/or
1106 inequality constraints and then projecting out the
1107 existentially quantified variables, if any.
1108 Constraints can be constructed, manipulated and
1109 added to (or removed from) (basic) sets and relations
1110 using the following functions.
1112 #include <isl/constraint.h>
1113 __isl_give isl_constraint *isl_equality_alloc(
1114 __isl_take isl_local_space *ls);
1115 __isl_give isl_constraint *isl_inequality_alloc(
1116 __isl_take isl_local_space *ls);
1117 __isl_give isl_constraint *isl_constraint_set_constant(
1118 __isl_take isl_constraint *constraint, isl_int v);
1119 __isl_give isl_constraint *isl_constraint_set_constant_si(
1120 __isl_take isl_constraint *constraint, int v);
1121 __isl_give isl_constraint *isl_constraint_set_coefficient(
1122 __isl_take isl_constraint *constraint,
1123 enum isl_dim_type type, int pos, isl_int v);
1124 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1125 __isl_take isl_constraint *constraint,
1126 enum isl_dim_type type, int pos, int v);
1127 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1128 __isl_take isl_basic_map *bmap,
1129 __isl_take isl_constraint *constraint);
1130 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1131 __isl_take isl_basic_set *bset,
1132 __isl_take isl_constraint *constraint);
1133 __isl_give isl_map *isl_map_add_constraint(
1134 __isl_take isl_map *map,
1135 __isl_take isl_constraint *constraint);
1136 __isl_give isl_set *isl_set_add_constraint(
1137 __isl_take isl_set *set,
1138 __isl_take isl_constraint *constraint);
1139 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1140 __isl_take isl_basic_set *bset,
1141 __isl_take isl_constraint *constraint);
1143 For example, to create a set containing the even integers
1144 between 10 and 42, you would use the following code.
1147 isl_local_space *ls;
1149 isl_basic_set *bset;
1151 space = isl_space_set_alloc(ctx, 0, 2);
1152 bset = isl_basic_set_universe(isl_space_copy(space));
1153 ls = isl_local_space_from_space(space);
1155 c = isl_equality_alloc(isl_local_space_copy(ls));
1156 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1157 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1158 bset = isl_basic_set_add_constraint(bset, c);
1160 c = isl_inequality_alloc(isl_local_space_copy(ls));
1161 c = isl_constraint_set_constant_si(c, -10);
1162 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1163 bset = isl_basic_set_add_constraint(bset, c);
1165 c = isl_inequality_alloc(ls);
1166 c = isl_constraint_set_constant_si(c, 42);
1167 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1168 bset = isl_basic_set_add_constraint(bset, c);
1170 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1174 isl_basic_set *bset;
1175 bset = isl_basic_set_read_from_str(ctx,
1176 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1178 A basic set or relation can also be constructed from two matrices
1179 describing the equalities and the inequalities.
1181 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1182 __isl_take isl_space *space,
1183 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1184 enum isl_dim_type c1,
1185 enum isl_dim_type c2, enum isl_dim_type c3,
1186 enum isl_dim_type c4);
1187 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1188 __isl_take isl_space *space,
1189 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1190 enum isl_dim_type c1,
1191 enum isl_dim_type c2, enum isl_dim_type c3,
1192 enum isl_dim_type c4, enum isl_dim_type c5);
1194 The C<isl_dim_type> arguments indicate the order in which
1195 different kinds of variables appear in the input matrices
1196 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1197 C<isl_dim_set> and C<isl_dim_div> for sets and
1198 of C<isl_dim_cst>, C<isl_dim_param>,
1199 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1201 A (basic) set or relation can also be constructed from a (piecewise)
1203 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1205 __isl_give isl_basic_map *isl_basic_map_from_aff(
1206 __isl_take isl_aff *aff);
1207 __isl_give isl_set *isl_set_from_pw_aff(
1208 __isl_take isl_pw_aff *pwaff);
1209 __isl_give isl_map *isl_map_from_pw_aff(
1210 __isl_take isl_pw_aff *pwaff);
1211 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1212 __isl_take isl_space *domain_space,
1213 __isl_take isl_aff_list *list);
1215 The C<domain_dim> argument describes the domain of the resulting
1216 basic relation. It is required because the C<list> may consist
1217 of zero affine expressions.
1219 =head2 Inspecting Sets and Relations
1221 Usually, the user should not have to care about the actual constraints
1222 of the sets and maps, but should instead apply the abstract operations
1223 explained in the following sections.
1224 Occasionally, however, it may be required to inspect the individual
1225 coefficients of the constraints. This section explains how to do so.
1226 In these cases, it may also be useful to have C<isl> compute
1227 an explicit representation of the existentially quantified variables.
1229 __isl_give isl_set *isl_set_compute_divs(
1230 __isl_take isl_set *set);
1231 __isl_give isl_map *isl_map_compute_divs(
1232 __isl_take isl_map *map);
1233 __isl_give isl_union_set *isl_union_set_compute_divs(
1234 __isl_take isl_union_set *uset);
1235 __isl_give isl_union_map *isl_union_map_compute_divs(
1236 __isl_take isl_union_map *umap);
1238 This explicit representation defines the existentially quantified
1239 variables as integer divisions of the other variables, possibly
1240 including earlier existentially quantified variables.
1241 An explicitly represented existentially quantified variable therefore
1242 has a unique value when the values of the other variables are known.
1243 If, furthermore, the same existentials, i.e., existentials
1244 with the same explicit representations, should appear in the
1245 same order in each of the disjuncts of a set or map, then the user should call
1246 either of the following functions.
1248 __isl_give isl_set *isl_set_align_divs(
1249 __isl_take isl_set *set);
1250 __isl_give isl_map *isl_map_align_divs(
1251 __isl_take isl_map *map);
1253 Alternatively, the existentially quantified variables can be removed
1254 using the following functions, which compute an overapproximation.
1256 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1257 __isl_take isl_basic_set *bset);
1258 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1259 __isl_take isl_basic_map *bmap);
1260 __isl_give isl_set *isl_set_remove_divs(
1261 __isl_take isl_set *set);
1262 __isl_give isl_map *isl_map_remove_divs(
1263 __isl_take isl_map *map);
1265 To iterate over all the sets or maps in a union set or map, use
1267 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1268 int (*fn)(__isl_take isl_set *set, void *user),
1270 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1271 int (*fn)(__isl_take isl_map *map, void *user),
1274 The number of sets or maps in a union set or map can be obtained
1277 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1278 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1280 To extract the set or map in a given space from a union, use
1282 __isl_give isl_set *isl_union_set_extract_set(
1283 __isl_keep isl_union_set *uset,
1284 __isl_take isl_space *space);
1285 __isl_give isl_map *isl_union_map_extract_map(
1286 __isl_keep isl_union_map *umap,
1287 __isl_take isl_space *space);
1289 To iterate over all the basic sets or maps in a set or map, use
1291 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1292 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1294 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1295 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1298 The callback function C<fn> should return 0 if successful and
1299 -1 if an error occurs. In the latter case, or if any other error
1300 occurs, the above functions will return -1.
1302 It should be noted that C<isl> does not guarantee that
1303 the basic sets or maps passed to C<fn> are disjoint.
1304 If this is required, then the user should call one of
1305 the following functions first.
1307 __isl_give isl_set *isl_set_make_disjoint(
1308 __isl_take isl_set *set);
1309 __isl_give isl_map *isl_map_make_disjoint(
1310 __isl_take isl_map *map);
1312 The number of basic sets in a set can be obtained
1315 int isl_set_n_basic_set(__isl_keep isl_set *set);
1317 To iterate over the constraints of a basic set or map, use
1319 #include <isl/constraint.h>
1321 int isl_basic_map_foreach_constraint(
1322 __isl_keep isl_basic_map *bmap,
1323 int (*fn)(__isl_take isl_constraint *c, void *user),
1325 void *isl_constraint_free(__isl_take isl_constraint *c);
1327 Again, the callback function C<fn> should return 0 if successful and
1328 -1 if an error occurs. In the latter case, or if any other error
1329 occurs, the above functions will return -1.
1330 The constraint C<c> represents either an equality or an inequality.
1331 Use the following function to find out whether a constraint
1332 represents an equality. If not, it represents an inequality.
1334 int isl_constraint_is_equality(
1335 __isl_keep isl_constraint *constraint);
1337 The coefficients of the constraints can be inspected using
1338 the following functions.
1340 void isl_constraint_get_constant(
1341 __isl_keep isl_constraint *constraint, isl_int *v);
1342 void isl_constraint_get_coefficient(
1343 __isl_keep isl_constraint *constraint,
1344 enum isl_dim_type type, int pos, isl_int *v);
1345 int isl_constraint_involves_dims(
1346 __isl_keep isl_constraint *constraint,
1347 enum isl_dim_type type, unsigned first, unsigned n);
1349 The explicit representations of the existentially quantified
1350 variables can be inspected using the following function.
1351 Note that the user is only allowed to use this function
1352 if the inspected set or map is the result of a call
1353 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1354 The existentially quantified variable is equal to the floor
1355 of the returned affine expression. The affine expression
1356 itself can be inspected using the functions in
1357 L<"Piecewise Quasi Affine Expressions">.
1359 __isl_give isl_aff *isl_constraint_get_div(
1360 __isl_keep isl_constraint *constraint, int pos);
1362 To obtain the constraints of a basic set or map in matrix
1363 form, use the following functions.
1365 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1366 __isl_keep isl_basic_set *bset,
1367 enum isl_dim_type c1, enum isl_dim_type c2,
1368 enum isl_dim_type c3, enum isl_dim_type c4);
1369 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1370 __isl_keep isl_basic_set *bset,
1371 enum isl_dim_type c1, enum isl_dim_type c2,
1372 enum isl_dim_type c3, enum isl_dim_type c4);
1373 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1374 __isl_keep isl_basic_map *bmap,
1375 enum isl_dim_type c1,
1376 enum isl_dim_type c2, enum isl_dim_type c3,
1377 enum isl_dim_type c4, enum isl_dim_type c5);
1378 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1379 __isl_keep isl_basic_map *bmap,
1380 enum isl_dim_type c1,
1381 enum isl_dim_type c2, enum isl_dim_type c3,
1382 enum isl_dim_type c4, enum isl_dim_type c5);
1384 The C<isl_dim_type> arguments dictate the order in which
1385 different kinds of variables appear in the resulting matrix
1386 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1387 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1389 The number of parameters, input, output or set dimensions can
1390 be obtained using the following functions.
1392 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1393 enum isl_dim_type type);
1394 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1395 enum isl_dim_type type);
1396 unsigned isl_set_dim(__isl_keep isl_set *set,
1397 enum isl_dim_type type);
1398 unsigned isl_map_dim(__isl_keep isl_map *map,
1399 enum isl_dim_type type);
1401 To check whether the description of a set or relation depends
1402 on one or more given dimensions, it is not necessary to iterate over all
1403 constraints. Instead the following functions can be used.
1405 int isl_basic_set_involves_dims(
1406 __isl_keep isl_basic_set *bset,
1407 enum isl_dim_type type, unsigned first, unsigned n);
1408 int isl_set_involves_dims(__isl_keep isl_set *set,
1409 enum isl_dim_type type, unsigned first, unsigned n);
1410 int isl_basic_map_involves_dims(
1411 __isl_keep isl_basic_map *bmap,
1412 enum isl_dim_type type, unsigned first, unsigned n);
1413 int isl_map_involves_dims(__isl_keep isl_map *map,
1414 enum isl_dim_type type, unsigned first, unsigned n);
1416 Similarly, the following functions can be used to check whether
1417 a given dimension is involved in any lower or upper bound.
1419 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1420 enum isl_dim_type type, unsigned pos);
1421 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1422 enum isl_dim_type type, unsigned pos);
1424 The identifiers or names of the domain and range spaces of a set
1425 or relation can be read off or set using the following functions.
1427 __isl_give isl_set *isl_set_set_tuple_id(
1428 __isl_take isl_set *set, __isl_take isl_id *id);
1429 __isl_give isl_set *isl_set_reset_tuple_id(
1430 __isl_take isl_set *set);
1431 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1432 __isl_give isl_id *isl_set_get_tuple_id(
1433 __isl_keep isl_set *set);
1434 __isl_give isl_map *isl_map_set_tuple_id(
1435 __isl_take isl_map *map, enum isl_dim_type type,
1436 __isl_take isl_id *id);
1437 __isl_give isl_map *isl_map_reset_tuple_id(
1438 __isl_take isl_map *map, enum isl_dim_type type);
1439 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1440 enum isl_dim_type type);
1441 __isl_give isl_id *isl_map_get_tuple_id(
1442 __isl_keep isl_map *map, enum isl_dim_type type);
1444 const char *isl_basic_set_get_tuple_name(
1445 __isl_keep isl_basic_set *bset);
1446 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1447 __isl_take isl_basic_set *set, const char *s);
1448 const char *isl_set_get_tuple_name(
1449 __isl_keep isl_set *set);
1450 const char *isl_basic_map_get_tuple_name(
1451 __isl_keep isl_basic_map *bmap,
1452 enum isl_dim_type type);
1453 const char *isl_map_get_tuple_name(
1454 __isl_keep isl_map *map,
1455 enum isl_dim_type type);
1457 As with C<isl_space_get_tuple_name>, the value returned points to
1458 an internal data structure.
1459 The identifiers, positions or names of individual dimensions can be
1460 read off using the following functions.
1462 __isl_give isl_set *isl_set_set_dim_id(
1463 __isl_take isl_set *set, enum isl_dim_type type,
1464 unsigned pos, __isl_take isl_id *id);
1465 int isl_set_has_dim_id(__isl_keep isl_set *set,
1466 enum isl_dim_type type, unsigned pos);
1467 __isl_give isl_id *isl_set_get_dim_id(
1468 __isl_keep isl_set *set, enum isl_dim_type type,
1470 __isl_give isl_map *isl_map_set_dim_id(
1471 __isl_take isl_map *map, enum isl_dim_type type,
1472 unsigned pos, __isl_take isl_id *id);
1473 int isl_map_has_dim_id(__isl_keep isl_map *map,
1474 enum isl_dim_type type, unsigned pos);
1475 __isl_give isl_id *isl_map_get_dim_id(
1476 __isl_keep isl_map *map, enum isl_dim_type type,
1479 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1480 enum isl_dim_type type, __isl_keep isl_id *id);
1481 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1482 enum isl_dim_type type, __isl_keep isl_id *id);
1483 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1484 enum isl_dim_type type, const char *name);
1486 const char *isl_constraint_get_dim_name(
1487 __isl_keep isl_constraint *constraint,
1488 enum isl_dim_type type, unsigned pos);
1489 const char *isl_basic_set_get_dim_name(
1490 __isl_keep isl_basic_set *bset,
1491 enum isl_dim_type type, unsigned pos);
1492 const char *isl_set_get_dim_name(
1493 __isl_keep isl_set *set,
1494 enum isl_dim_type type, unsigned pos);
1495 const char *isl_basic_map_get_dim_name(
1496 __isl_keep isl_basic_map *bmap,
1497 enum isl_dim_type type, unsigned pos);
1498 const char *isl_map_get_dim_name(
1499 __isl_keep isl_map *map,
1500 enum isl_dim_type type, unsigned pos);
1502 These functions are mostly useful to obtain the identifiers, positions
1503 or names of the parameters. Identifiers of individual dimensions are
1504 essentially only useful for printing. They are ignored by all other
1505 operations and may not be preserved across those operations.
1509 =head3 Unary Properties
1515 The following functions test whether the given set or relation
1516 contains any integer points. The ``plain'' variants do not perform
1517 any computations, but simply check if the given set or relation
1518 is already known to be empty.
1520 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1521 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1522 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1523 int isl_set_is_empty(__isl_keep isl_set *set);
1524 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1525 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1526 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1527 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1528 int isl_map_is_empty(__isl_keep isl_map *map);
1529 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1531 =item * Universality
1533 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1534 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1535 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1537 =item * Single-valuedness
1539 int isl_map_is_single_valued(__isl_keep isl_map *map);
1540 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1544 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1545 int isl_map_is_injective(__isl_keep isl_map *map);
1546 int isl_union_map_plain_is_injective(
1547 __isl_keep isl_union_map *umap);
1548 int isl_union_map_is_injective(
1549 __isl_keep isl_union_map *umap);
1553 int isl_map_is_bijective(__isl_keep isl_map *map);
1554 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1558 int isl_basic_map_plain_is_fixed(
1559 __isl_keep isl_basic_map *bmap,
1560 enum isl_dim_type type, unsigned pos,
1562 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1563 enum isl_dim_type type, unsigned pos,
1565 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1566 enum isl_dim_type type, unsigned pos,
1569 Check if the relation obviously lies on a hyperplane where the given dimension
1570 has a fixed value and if so, return that value in C<*val>.
1574 To check whether a set is a parameter domain, use this function:
1576 int isl_set_is_params(__isl_keep isl_set *set);
1580 The following functions check whether the domain of the given
1581 (basic) set is a wrapped relation.
1583 int isl_basic_set_is_wrapping(
1584 __isl_keep isl_basic_set *bset);
1585 int isl_set_is_wrapping(__isl_keep isl_set *set);
1587 =item * Internal Product
1589 int isl_basic_map_can_zip(
1590 __isl_keep isl_basic_map *bmap);
1591 int isl_map_can_zip(__isl_keep isl_map *map);
1593 Check whether the product of domain and range of the given relation
1595 i.e., whether both domain and range are nested relations.
1599 =head3 Binary Properties
1605 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1606 __isl_keep isl_set *set2);
1607 int isl_set_is_equal(__isl_keep isl_set *set1,
1608 __isl_keep isl_set *set2);
1609 int isl_union_set_is_equal(
1610 __isl_keep isl_union_set *uset1,
1611 __isl_keep isl_union_set *uset2);
1612 int isl_basic_map_is_equal(
1613 __isl_keep isl_basic_map *bmap1,
1614 __isl_keep isl_basic_map *bmap2);
1615 int isl_map_is_equal(__isl_keep isl_map *map1,
1616 __isl_keep isl_map *map2);
1617 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1618 __isl_keep isl_map *map2);
1619 int isl_union_map_is_equal(
1620 __isl_keep isl_union_map *umap1,
1621 __isl_keep isl_union_map *umap2);
1623 =item * Disjointness
1625 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1626 __isl_keep isl_set *set2);
1630 int isl_set_is_subset(__isl_keep isl_set *set1,
1631 __isl_keep isl_set *set2);
1632 int isl_set_is_strict_subset(
1633 __isl_keep isl_set *set1,
1634 __isl_keep isl_set *set2);
1635 int isl_union_set_is_subset(
1636 __isl_keep isl_union_set *uset1,
1637 __isl_keep isl_union_set *uset2);
1638 int isl_union_set_is_strict_subset(
1639 __isl_keep isl_union_set *uset1,
1640 __isl_keep isl_union_set *uset2);
1641 int isl_basic_map_is_subset(
1642 __isl_keep isl_basic_map *bmap1,
1643 __isl_keep isl_basic_map *bmap2);
1644 int isl_basic_map_is_strict_subset(
1645 __isl_keep isl_basic_map *bmap1,
1646 __isl_keep isl_basic_map *bmap2);
1647 int isl_map_is_subset(
1648 __isl_keep isl_map *map1,
1649 __isl_keep isl_map *map2);
1650 int isl_map_is_strict_subset(
1651 __isl_keep isl_map *map1,
1652 __isl_keep isl_map *map2);
1653 int isl_union_map_is_subset(
1654 __isl_keep isl_union_map *umap1,
1655 __isl_keep isl_union_map *umap2);
1656 int isl_union_map_is_strict_subset(
1657 __isl_keep isl_union_map *umap1,
1658 __isl_keep isl_union_map *umap2);
1662 =head2 Unary Operations
1668 __isl_give isl_set *isl_set_complement(
1669 __isl_take isl_set *set);
1673 __isl_give isl_basic_map *isl_basic_map_reverse(
1674 __isl_take isl_basic_map *bmap);
1675 __isl_give isl_map *isl_map_reverse(
1676 __isl_take isl_map *map);
1677 __isl_give isl_union_map *isl_union_map_reverse(
1678 __isl_take isl_union_map *umap);
1682 __isl_give isl_basic_set *isl_basic_set_project_out(
1683 __isl_take isl_basic_set *bset,
1684 enum isl_dim_type type, unsigned first, unsigned n);
1685 __isl_give isl_basic_map *isl_basic_map_project_out(
1686 __isl_take isl_basic_map *bmap,
1687 enum isl_dim_type type, unsigned first, unsigned n);
1688 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1689 enum isl_dim_type type, unsigned first, unsigned n);
1690 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1691 enum isl_dim_type type, unsigned first, unsigned n);
1692 __isl_give isl_basic_set *isl_basic_set_params(
1693 __isl_take isl_basic_set *bset);
1694 __isl_give isl_basic_set *isl_basic_map_domain(
1695 __isl_take isl_basic_map *bmap);
1696 __isl_give isl_basic_set *isl_basic_map_range(
1697 __isl_take isl_basic_map *bmap);
1698 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1699 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1700 __isl_give isl_set *isl_map_domain(
1701 __isl_take isl_map *bmap);
1702 __isl_give isl_set *isl_map_range(
1703 __isl_take isl_map *map);
1704 __isl_give isl_union_set *isl_union_map_domain(
1705 __isl_take isl_union_map *umap);
1706 __isl_give isl_union_set *isl_union_map_range(
1707 __isl_take isl_union_map *umap);
1709 __isl_give isl_basic_map *isl_basic_map_domain_map(
1710 __isl_take isl_basic_map *bmap);
1711 __isl_give isl_basic_map *isl_basic_map_range_map(
1712 __isl_take isl_basic_map *bmap);
1713 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1714 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1715 __isl_give isl_union_map *isl_union_map_domain_map(
1716 __isl_take isl_union_map *umap);
1717 __isl_give isl_union_map *isl_union_map_range_map(
1718 __isl_take isl_union_map *umap);
1720 The functions above construct a (basic, regular or union) relation
1721 that maps (a wrapped version of) the input relation to its domain or range.
1725 __isl_give isl_set *isl_set_eliminate(
1726 __isl_take isl_set *set, enum isl_dim_type type,
1727 unsigned first, unsigned n);
1729 Eliminate the coefficients for the given dimensions from the constraints,
1730 without removing the dimensions.
1734 __isl_give isl_basic_set *isl_basic_set_fix(
1735 __isl_take isl_basic_set *bset,
1736 enum isl_dim_type type, unsigned pos,
1738 __isl_give isl_basic_set *isl_basic_set_fix_si(
1739 __isl_take isl_basic_set *bset,
1740 enum isl_dim_type type, unsigned pos, int value);
1741 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1742 enum isl_dim_type type, unsigned pos,
1744 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1745 enum isl_dim_type type, unsigned pos, int value);
1746 __isl_give isl_basic_map *isl_basic_map_fix_si(
1747 __isl_take isl_basic_map *bmap,
1748 enum isl_dim_type type, unsigned pos, int value);
1749 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1750 enum isl_dim_type type, unsigned pos, int value);
1752 Intersect the set or relation with the hyperplane where the given
1753 dimension has the fixed given value.
1755 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1756 enum isl_dim_type type1, int pos1,
1757 enum isl_dim_type type2, int pos2);
1758 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1759 enum isl_dim_type type1, int pos1,
1760 enum isl_dim_type type2, int pos2);
1762 Intersect the set or relation with the hyperplane where the given
1763 dimensions are equal to each other.
1765 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1766 enum isl_dim_type type1, int pos1,
1767 enum isl_dim_type type2, int pos2);
1769 Intersect the relation with the hyperplane where the given
1770 dimensions have opposite values.
1774 __isl_give isl_map *isl_set_identity(
1775 __isl_take isl_set *set);
1776 __isl_give isl_union_map *isl_union_set_identity(
1777 __isl_take isl_union_set *uset);
1779 Construct an identity relation on the given (union) set.
1783 __isl_give isl_basic_set *isl_basic_map_deltas(
1784 __isl_take isl_basic_map *bmap);
1785 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1786 __isl_give isl_union_set *isl_union_map_deltas(
1787 __isl_take isl_union_map *umap);
1789 These functions return a (basic) set containing the differences
1790 between image elements and corresponding domain elements in the input.
1792 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1793 __isl_take isl_basic_map *bmap);
1794 __isl_give isl_map *isl_map_deltas_map(
1795 __isl_take isl_map *map);
1796 __isl_give isl_union_map *isl_union_map_deltas_map(
1797 __isl_take isl_union_map *umap);
1799 The functions above construct a (basic, regular or union) relation
1800 that maps (a wrapped version of) the input relation to its delta set.
1804 Simplify the representation of a set or relation by trying
1805 to combine pairs of basic sets or relations into a single
1806 basic set or relation.
1808 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1809 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1810 __isl_give isl_union_set *isl_union_set_coalesce(
1811 __isl_take isl_union_set *uset);
1812 __isl_give isl_union_map *isl_union_map_coalesce(
1813 __isl_take isl_union_map *umap);
1815 =item * Detecting equalities
1817 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1818 __isl_take isl_basic_set *bset);
1819 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1820 __isl_take isl_basic_map *bmap);
1821 __isl_give isl_set *isl_set_detect_equalities(
1822 __isl_take isl_set *set);
1823 __isl_give isl_map *isl_map_detect_equalities(
1824 __isl_take isl_map *map);
1825 __isl_give isl_union_set *isl_union_set_detect_equalities(
1826 __isl_take isl_union_set *uset);
1827 __isl_give isl_union_map *isl_union_map_detect_equalities(
1828 __isl_take isl_union_map *umap);
1830 Simplify the representation of a set or relation by detecting implicit
1833 =item * Removing redundant constraints
1835 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1836 __isl_take isl_basic_set *bset);
1837 __isl_give isl_set *isl_set_remove_redundancies(
1838 __isl_take isl_set *set);
1839 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1840 __isl_take isl_basic_map *bmap);
1841 __isl_give isl_map *isl_map_remove_redundancies(
1842 __isl_take isl_map *map);
1846 __isl_give isl_basic_set *isl_set_convex_hull(
1847 __isl_take isl_set *set);
1848 __isl_give isl_basic_map *isl_map_convex_hull(
1849 __isl_take isl_map *map);
1851 If the input set or relation has any existentially quantified
1852 variables, then the result of these operations is currently undefined.
1856 __isl_give isl_basic_set *isl_set_simple_hull(
1857 __isl_take isl_set *set);
1858 __isl_give isl_basic_map *isl_map_simple_hull(
1859 __isl_take isl_map *map);
1860 __isl_give isl_union_map *isl_union_map_simple_hull(
1861 __isl_take isl_union_map *umap);
1863 These functions compute a single basic set or relation
1864 that contains the whole input set or relation.
1865 In particular, the output is described by translates
1866 of the constraints describing the basic sets or relations in the input.
1870 (See \autoref{s:simple hull}.)
1876 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1877 __isl_take isl_basic_set *bset);
1878 __isl_give isl_basic_set *isl_set_affine_hull(
1879 __isl_take isl_set *set);
1880 __isl_give isl_union_set *isl_union_set_affine_hull(
1881 __isl_take isl_union_set *uset);
1882 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1883 __isl_take isl_basic_map *bmap);
1884 __isl_give isl_basic_map *isl_map_affine_hull(
1885 __isl_take isl_map *map);
1886 __isl_give isl_union_map *isl_union_map_affine_hull(
1887 __isl_take isl_union_map *umap);
1889 In case of union sets and relations, the affine hull is computed
1892 =item * Polyhedral hull
1894 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1895 __isl_take isl_set *set);
1896 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1897 __isl_take isl_map *map);
1898 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1899 __isl_take isl_union_set *uset);
1900 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1901 __isl_take isl_union_map *umap);
1903 These functions compute a single basic set or relation
1904 not involving any existentially quantified variables
1905 that contains the whole input set or relation.
1906 In case of union sets and relations, the polyhedral hull is computed
1909 =item * Optimization
1911 #include <isl/ilp.h>
1912 enum isl_lp_result isl_basic_set_max(
1913 __isl_keep isl_basic_set *bset,
1914 __isl_keep isl_aff *obj, isl_int *opt)
1915 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1916 __isl_keep isl_aff *obj, isl_int *opt);
1917 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1918 __isl_keep isl_aff *obj, isl_int *opt);
1920 Compute the minimum or maximum of the integer affine expression C<obj>
1921 over the points in C<set>, returning the result in C<opt>.
1922 The return value may be one of C<isl_lp_error>,
1923 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1925 =item * Parametric optimization
1927 __isl_give isl_pw_aff *isl_set_dim_min(
1928 __isl_take isl_set *set, int pos);
1929 __isl_give isl_pw_aff *isl_set_dim_max(
1930 __isl_take isl_set *set, int pos);
1932 Compute the minimum or maximum of the given set dimension as a function of the
1933 parameters, but independently of the other set dimensions.
1934 For lexicographic optimization, see L<"Lexicographic Optimization">.
1938 The following functions compute either the set of (rational) coefficient
1939 values of valid constraints for the given set or the set of (rational)
1940 values satisfying the constraints with coefficients from the given set.
1941 Internally, these two sets of functions perform essentially the
1942 same operations, except that the set of coefficients is assumed to
1943 be a cone, while the set of values may be any polyhedron.
1944 The current implementation is based on the Farkas lemma and
1945 Fourier-Motzkin elimination, but this may change or be made optional
1946 in future. In particular, future implementations may use different
1947 dualization algorithms or skip the elimination step.
1949 __isl_give isl_basic_set *isl_basic_set_coefficients(
1950 __isl_take isl_basic_set *bset);
1951 __isl_give isl_basic_set *isl_set_coefficients(
1952 __isl_take isl_set *set);
1953 __isl_give isl_union_set *isl_union_set_coefficients(
1954 __isl_take isl_union_set *bset);
1955 __isl_give isl_basic_set *isl_basic_set_solutions(
1956 __isl_take isl_basic_set *bset);
1957 __isl_give isl_basic_set *isl_set_solutions(
1958 __isl_take isl_set *set);
1959 __isl_give isl_union_set *isl_union_set_solutions(
1960 __isl_take isl_union_set *bset);
1964 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1966 __isl_give isl_union_map *isl_union_map_power(
1967 __isl_take isl_union_map *umap, int *exact);
1969 Compute a parametric representation for all positive powers I<k> of C<map>.
1970 The result maps I<k> to a nested relation corresponding to the
1971 I<k>th power of C<map>.
1972 The result may be an overapproximation. If the result is known to be exact,
1973 then C<*exact> is set to C<1>.
1975 =item * Transitive closure
1977 __isl_give isl_map *isl_map_transitive_closure(
1978 __isl_take isl_map *map, int *exact);
1979 __isl_give isl_union_map *isl_union_map_transitive_closure(
1980 __isl_take isl_union_map *umap, int *exact);
1982 Compute the transitive closure of C<map>.
1983 The result may be an overapproximation. If the result is known to be exact,
1984 then C<*exact> is set to C<1>.
1986 =item * Reaching path lengths
1988 __isl_give isl_map *isl_map_reaching_path_lengths(
1989 __isl_take isl_map *map, int *exact);
1991 Compute a relation that maps each element in the range of C<map>
1992 to the lengths of all paths composed of edges in C<map> that
1993 end up in the given element.
1994 The result may be an overapproximation. If the result is known to be exact,
1995 then C<*exact> is set to C<1>.
1996 To compute the I<maximal> path length, the resulting relation
1997 should be postprocessed by C<isl_map_lexmax>.
1998 In particular, if the input relation is a dependence relation
1999 (mapping sources to sinks), then the maximal path length corresponds
2000 to the free schedule.
2001 Note, however, that C<isl_map_lexmax> expects the maximum to be
2002 finite, so if the path lengths are unbounded (possibly due to
2003 the overapproximation), then you will get an error message.
2007 __isl_give isl_basic_set *isl_basic_map_wrap(
2008 __isl_take isl_basic_map *bmap);
2009 __isl_give isl_set *isl_map_wrap(
2010 __isl_take isl_map *map);
2011 __isl_give isl_union_set *isl_union_map_wrap(
2012 __isl_take isl_union_map *umap);
2013 __isl_give isl_basic_map *isl_basic_set_unwrap(
2014 __isl_take isl_basic_set *bset);
2015 __isl_give isl_map *isl_set_unwrap(
2016 __isl_take isl_set *set);
2017 __isl_give isl_union_map *isl_union_set_unwrap(
2018 __isl_take isl_union_set *uset);
2022 Remove any internal structure of domain (and range) of the given
2023 set or relation. If there is any such internal structure in the input,
2024 then the name of the space is also removed.
2026 __isl_give isl_basic_set *isl_basic_set_flatten(
2027 __isl_take isl_basic_set *bset);
2028 __isl_give isl_set *isl_set_flatten(
2029 __isl_take isl_set *set);
2030 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2031 __isl_take isl_basic_map *bmap);
2032 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2033 __isl_take isl_basic_map *bmap);
2034 __isl_give isl_map *isl_map_flatten_range(
2035 __isl_take isl_map *map);
2036 __isl_give isl_map *isl_map_flatten_domain(
2037 __isl_take isl_map *map);
2038 __isl_give isl_basic_map *isl_basic_map_flatten(
2039 __isl_take isl_basic_map *bmap);
2040 __isl_give isl_map *isl_map_flatten(
2041 __isl_take isl_map *map);
2043 __isl_give isl_map *isl_set_flatten_map(
2044 __isl_take isl_set *set);
2046 The function above constructs a relation
2047 that maps the input set to a flattened version of the set.
2051 Lift the input set to a space with extra dimensions corresponding
2052 to the existentially quantified variables in the input.
2053 In particular, the result lives in a wrapped map where the domain
2054 is the original space and the range corresponds to the original
2055 existentially quantified variables.
2057 __isl_give isl_basic_set *isl_basic_set_lift(
2058 __isl_take isl_basic_set *bset);
2059 __isl_give isl_set *isl_set_lift(
2060 __isl_take isl_set *set);
2061 __isl_give isl_union_set *isl_union_set_lift(
2062 __isl_take isl_union_set *uset);
2064 =item * Internal Product
2066 __isl_give isl_basic_map *isl_basic_map_zip(
2067 __isl_take isl_basic_map *bmap);
2068 __isl_give isl_map *isl_map_zip(
2069 __isl_take isl_map *map);
2070 __isl_give isl_union_map *isl_union_map_zip(
2071 __isl_take isl_union_map *umap);
2073 Given a relation with nested relations for domain and range,
2074 interchange the range of the domain with the domain of the range.
2076 =item * Aligning parameters
2078 __isl_give isl_set *isl_set_align_params(
2079 __isl_take isl_set *set,
2080 __isl_take isl_space *model);
2081 __isl_give isl_map *isl_map_align_params(
2082 __isl_take isl_map *map,
2083 __isl_take isl_space *model);
2085 Change the order of the parameters of the given set or relation
2086 such that the first parameters match those of C<model>.
2087 This may involve the introduction of extra parameters.
2088 All parameters need to be named.
2090 =item * Dimension manipulation
2092 __isl_give isl_set *isl_set_add_dims(
2093 __isl_take isl_set *set,
2094 enum isl_dim_type type, unsigned n);
2095 __isl_give isl_map *isl_map_add_dims(
2096 __isl_take isl_map *map,
2097 enum isl_dim_type type, unsigned n);
2098 __isl_give isl_set *isl_set_insert_dims(
2099 __isl_take isl_set *set,
2100 enum isl_dim_type type, unsigned pos, unsigned n);
2101 __isl_give isl_map *isl_map_insert_dims(
2102 __isl_take isl_map *map,
2103 enum isl_dim_type type, unsigned pos, unsigned n);
2104 __isl_give isl_basic_set *isl_basic_set_move_dims(
2105 __isl_take isl_basic_set *bset,
2106 enum isl_dim_type dst_type, unsigned dst_pos,
2107 enum isl_dim_type src_type, unsigned src_pos,
2109 __isl_give isl_basic_map *isl_basic_map_move_dims(
2110 __isl_take isl_basic_map *bmap,
2111 enum isl_dim_type dst_type, unsigned dst_pos,
2112 enum isl_dim_type src_type, unsigned src_pos,
2114 __isl_give isl_set *isl_set_move_dims(
2115 __isl_take isl_set *set,
2116 enum isl_dim_type dst_type, unsigned dst_pos,
2117 enum isl_dim_type src_type, unsigned src_pos,
2119 __isl_give isl_map *isl_map_move_dims(
2120 __isl_take isl_map *map,
2121 enum isl_dim_type dst_type, unsigned dst_pos,
2122 enum isl_dim_type src_type, unsigned src_pos,
2125 It is usually not advisable to directly change the (input or output)
2126 space of a set or a relation as this removes the name and the internal
2127 structure of the space. However, the above functions can be useful
2128 to add new parameters, assuming
2129 C<isl_set_align_params> and C<isl_map_align_params>
2134 =head2 Binary Operations
2136 The two arguments of a binary operation not only need to live
2137 in the same C<isl_ctx>, they currently also need to have
2138 the same (number of) parameters.
2140 =head3 Basic Operations
2144 =item * Intersection
2146 __isl_give isl_basic_set *isl_basic_set_intersect(
2147 __isl_take isl_basic_set *bset1,
2148 __isl_take isl_basic_set *bset2);
2149 __isl_give isl_set *isl_set_intersect_params(
2150 __isl_take isl_set *set,
2151 __isl_take isl_set *params);
2152 __isl_give isl_set *isl_set_intersect(
2153 __isl_take isl_set *set1,
2154 __isl_take isl_set *set2);
2155 __isl_give isl_union_set *isl_union_set_intersect(
2156 __isl_take isl_union_set *uset1,
2157 __isl_take isl_union_set *uset2);
2158 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2159 __isl_take isl_basic_map *bmap,
2160 __isl_take isl_basic_set *bset);
2161 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2162 __isl_take isl_basic_map *bmap,
2163 __isl_take isl_basic_set *bset);
2164 __isl_give isl_basic_map *isl_basic_map_intersect(
2165 __isl_take isl_basic_map *bmap1,
2166 __isl_take isl_basic_map *bmap2);
2167 __isl_give isl_map *isl_map_intersect_params(
2168 __isl_take isl_map *map,
2169 __isl_take isl_set *params);
2170 __isl_give isl_map *isl_map_intersect_domain(
2171 __isl_take isl_map *map,
2172 __isl_take isl_set *set);
2173 __isl_give isl_map *isl_map_intersect_range(
2174 __isl_take isl_map *map,
2175 __isl_take isl_set *set);
2176 __isl_give isl_map *isl_map_intersect(
2177 __isl_take isl_map *map1,
2178 __isl_take isl_map *map2);
2179 __isl_give isl_union_map *isl_union_map_intersect_domain(
2180 __isl_take isl_union_map *umap,
2181 __isl_take isl_union_set *uset);
2182 __isl_give isl_union_map *isl_union_map_intersect_range(
2183 __isl_take isl_union_map *umap,
2184 __isl_take isl_union_set *uset);
2185 __isl_give isl_union_map *isl_union_map_intersect(
2186 __isl_take isl_union_map *umap1,
2187 __isl_take isl_union_map *umap2);
2191 __isl_give isl_set *isl_basic_set_union(
2192 __isl_take isl_basic_set *bset1,
2193 __isl_take isl_basic_set *bset2);
2194 __isl_give isl_map *isl_basic_map_union(
2195 __isl_take isl_basic_map *bmap1,
2196 __isl_take isl_basic_map *bmap2);
2197 __isl_give isl_set *isl_set_union(
2198 __isl_take isl_set *set1,
2199 __isl_take isl_set *set2);
2200 __isl_give isl_map *isl_map_union(
2201 __isl_take isl_map *map1,
2202 __isl_take isl_map *map2);
2203 __isl_give isl_union_set *isl_union_set_union(
2204 __isl_take isl_union_set *uset1,
2205 __isl_take isl_union_set *uset2);
2206 __isl_give isl_union_map *isl_union_map_union(
2207 __isl_take isl_union_map *umap1,
2208 __isl_take isl_union_map *umap2);
2210 =item * Set difference
2212 __isl_give isl_set *isl_set_subtract(
2213 __isl_take isl_set *set1,
2214 __isl_take isl_set *set2);
2215 __isl_give isl_map *isl_map_subtract(
2216 __isl_take isl_map *map1,
2217 __isl_take isl_map *map2);
2218 __isl_give isl_union_set *isl_union_set_subtract(
2219 __isl_take isl_union_set *uset1,
2220 __isl_take isl_union_set *uset2);
2221 __isl_give isl_union_map *isl_union_map_subtract(
2222 __isl_take isl_union_map *umap1,
2223 __isl_take isl_union_map *umap2);
2227 __isl_give isl_basic_set *isl_basic_set_apply(
2228 __isl_take isl_basic_set *bset,
2229 __isl_take isl_basic_map *bmap);
2230 __isl_give isl_set *isl_set_apply(
2231 __isl_take isl_set *set,
2232 __isl_take isl_map *map);
2233 __isl_give isl_union_set *isl_union_set_apply(
2234 __isl_take isl_union_set *uset,
2235 __isl_take isl_union_map *umap);
2236 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2237 __isl_take isl_basic_map *bmap1,
2238 __isl_take isl_basic_map *bmap2);
2239 __isl_give isl_basic_map *isl_basic_map_apply_range(
2240 __isl_take isl_basic_map *bmap1,
2241 __isl_take isl_basic_map *bmap2);
2242 __isl_give isl_map *isl_map_apply_domain(
2243 __isl_take isl_map *map1,
2244 __isl_take isl_map *map2);
2245 __isl_give isl_union_map *isl_union_map_apply_domain(
2246 __isl_take isl_union_map *umap1,
2247 __isl_take isl_union_map *umap2);
2248 __isl_give isl_map *isl_map_apply_range(
2249 __isl_take isl_map *map1,
2250 __isl_take isl_map *map2);
2251 __isl_give isl_union_map *isl_union_map_apply_range(
2252 __isl_take isl_union_map *umap1,
2253 __isl_take isl_union_map *umap2);
2255 =item * Cartesian Product
2257 __isl_give isl_set *isl_set_product(
2258 __isl_take isl_set *set1,
2259 __isl_take isl_set *set2);
2260 __isl_give isl_union_set *isl_union_set_product(
2261 __isl_take isl_union_set *uset1,
2262 __isl_take isl_union_set *uset2);
2263 __isl_give isl_basic_map *isl_basic_map_domain_product(
2264 __isl_take isl_basic_map *bmap1,
2265 __isl_take isl_basic_map *bmap2);
2266 __isl_give isl_basic_map *isl_basic_map_range_product(
2267 __isl_take isl_basic_map *bmap1,
2268 __isl_take isl_basic_map *bmap2);
2269 __isl_give isl_map *isl_map_domain_product(
2270 __isl_take isl_map *map1,
2271 __isl_take isl_map *map2);
2272 __isl_give isl_map *isl_map_range_product(
2273 __isl_take isl_map *map1,
2274 __isl_take isl_map *map2);
2275 __isl_give isl_union_map *isl_union_map_range_product(
2276 __isl_take isl_union_map *umap1,
2277 __isl_take isl_union_map *umap2);
2278 __isl_give isl_map *isl_map_product(
2279 __isl_take isl_map *map1,
2280 __isl_take isl_map *map2);
2281 __isl_give isl_union_map *isl_union_map_product(
2282 __isl_take isl_union_map *umap1,
2283 __isl_take isl_union_map *umap2);
2285 The above functions compute the cross product of the given
2286 sets or relations. The domains and ranges of the results
2287 are wrapped maps between domains and ranges of the inputs.
2288 To obtain a ``flat'' product, use the following functions
2291 __isl_give isl_basic_set *isl_basic_set_flat_product(
2292 __isl_take isl_basic_set *bset1,
2293 __isl_take isl_basic_set *bset2);
2294 __isl_give isl_set *isl_set_flat_product(
2295 __isl_take isl_set *set1,
2296 __isl_take isl_set *set2);
2297 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2298 __isl_take isl_basic_map *bmap1,
2299 __isl_take isl_basic_map *bmap2);
2300 __isl_give isl_map *isl_map_flat_domain_product(
2301 __isl_take isl_map *map1,
2302 __isl_take isl_map *map2);
2303 __isl_give isl_map *isl_map_flat_range_product(
2304 __isl_take isl_map *map1,
2305 __isl_take isl_map *map2);
2306 __isl_give isl_union_map *isl_union_map_flat_range_product(
2307 __isl_take isl_union_map *umap1,
2308 __isl_take isl_union_map *umap2);
2309 __isl_give isl_basic_map *isl_basic_map_flat_product(
2310 __isl_take isl_basic_map *bmap1,
2311 __isl_take isl_basic_map *bmap2);
2312 __isl_give isl_map *isl_map_flat_product(
2313 __isl_take isl_map *map1,
2314 __isl_take isl_map *map2);
2316 =item * Simplification
2318 __isl_give isl_basic_set *isl_basic_set_gist(
2319 __isl_take isl_basic_set *bset,
2320 __isl_take isl_basic_set *context);
2321 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2322 __isl_take isl_set *context);
2323 __isl_give isl_set *isl_set_gist_params(
2324 __isl_take isl_set *set,
2325 __isl_take isl_set *context);
2326 __isl_give isl_union_set *isl_union_set_gist(
2327 __isl_take isl_union_set *uset,
2328 __isl_take isl_union_set *context);
2329 __isl_give isl_basic_map *isl_basic_map_gist(
2330 __isl_take isl_basic_map *bmap,
2331 __isl_take isl_basic_map *context);
2332 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2333 __isl_take isl_map *context);
2334 __isl_give isl_map *isl_map_gist_params(
2335 __isl_take isl_map *map,
2336 __isl_take isl_set *context);
2337 __isl_give isl_union_map *isl_union_map_gist(
2338 __isl_take isl_union_map *umap,
2339 __isl_take isl_union_map *context);
2341 The gist operation returns a set or relation that has the
2342 same intersection with the context as the input set or relation.
2343 Any implicit equality in the intersection is made explicit in the result,
2344 while all inequalities that are redundant with respect to the intersection
2346 In case of union sets and relations, the gist operation is performed
2351 =head3 Lexicographic Optimization
2353 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2354 the following functions
2355 compute a set that contains the lexicographic minimum or maximum
2356 of the elements in C<set> (or C<bset>) for those values of the parameters
2357 that satisfy C<dom>.
2358 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2359 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2361 In other words, the union of the parameter values
2362 for which the result is non-empty and of C<*empty>
2365 __isl_give isl_set *isl_basic_set_partial_lexmin(
2366 __isl_take isl_basic_set *bset,
2367 __isl_take isl_basic_set *dom,
2368 __isl_give isl_set **empty);
2369 __isl_give isl_set *isl_basic_set_partial_lexmax(
2370 __isl_take isl_basic_set *bset,
2371 __isl_take isl_basic_set *dom,
2372 __isl_give isl_set **empty);
2373 __isl_give isl_set *isl_set_partial_lexmin(
2374 __isl_take isl_set *set, __isl_take isl_set *dom,
2375 __isl_give isl_set **empty);
2376 __isl_give isl_set *isl_set_partial_lexmax(
2377 __isl_take isl_set *set, __isl_take isl_set *dom,
2378 __isl_give isl_set **empty);
2380 Given a (basic) set C<set> (or C<bset>), the following functions simply
2381 return a set containing the lexicographic minimum or maximum
2382 of the elements in C<set> (or C<bset>).
2383 In case of union sets, the optimum is computed per space.
2385 __isl_give isl_set *isl_basic_set_lexmin(
2386 __isl_take isl_basic_set *bset);
2387 __isl_give isl_set *isl_basic_set_lexmax(
2388 __isl_take isl_basic_set *bset);
2389 __isl_give isl_set *isl_set_lexmin(
2390 __isl_take isl_set *set);
2391 __isl_give isl_set *isl_set_lexmax(
2392 __isl_take isl_set *set);
2393 __isl_give isl_union_set *isl_union_set_lexmin(
2394 __isl_take isl_union_set *uset);
2395 __isl_give isl_union_set *isl_union_set_lexmax(
2396 __isl_take isl_union_set *uset);
2398 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2399 the following functions
2400 compute a relation that maps each element of C<dom>
2401 to the single lexicographic minimum or maximum
2402 of the elements that are associated to that same
2403 element in C<map> (or C<bmap>).
2404 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2405 that contains the elements in C<dom> that do not map
2406 to any elements in C<map> (or C<bmap>).
2407 In other words, the union of the domain of the result and of C<*empty>
2410 __isl_give isl_map *isl_basic_map_partial_lexmax(
2411 __isl_take isl_basic_map *bmap,
2412 __isl_take isl_basic_set *dom,
2413 __isl_give isl_set **empty);
2414 __isl_give isl_map *isl_basic_map_partial_lexmin(
2415 __isl_take isl_basic_map *bmap,
2416 __isl_take isl_basic_set *dom,
2417 __isl_give isl_set **empty);
2418 __isl_give isl_map *isl_map_partial_lexmax(
2419 __isl_take isl_map *map, __isl_take isl_set *dom,
2420 __isl_give isl_set **empty);
2421 __isl_give isl_map *isl_map_partial_lexmin(
2422 __isl_take isl_map *map, __isl_take isl_set *dom,
2423 __isl_give isl_set **empty);
2425 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2426 return a map mapping each element in the domain of
2427 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2428 of all elements associated to that element.
2429 In case of union relations, the optimum is computed per space.
2431 __isl_give isl_map *isl_basic_map_lexmin(
2432 __isl_take isl_basic_map *bmap);
2433 __isl_give isl_map *isl_basic_map_lexmax(
2434 __isl_take isl_basic_map *bmap);
2435 __isl_give isl_map *isl_map_lexmin(
2436 __isl_take isl_map *map);
2437 __isl_give isl_map *isl_map_lexmax(
2438 __isl_take isl_map *map);
2439 __isl_give isl_union_map *isl_union_map_lexmin(
2440 __isl_take isl_union_map *umap);
2441 __isl_give isl_union_map *isl_union_map_lexmax(
2442 __isl_take isl_union_map *umap);
2446 Lists are defined over several element types, including
2447 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2448 Here we take lists of C<isl_set>s as an example.
2449 Lists can be created, copied and freed using the following functions.
2451 #include <isl/list.h>
2452 __isl_give isl_set_list *isl_set_list_from_set(
2453 __isl_take isl_set *el);
2454 __isl_give isl_set_list *isl_set_list_alloc(
2455 isl_ctx *ctx, int n);
2456 __isl_give isl_set_list *isl_set_list_copy(
2457 __isl_keep isl_set_list *list);
2458 __isl_give isl_set_list *isl_set_list_add(
2459 __isl_take isl_set_list *list,
2460 __isl_take isl_set *el);
2461 __isl_give isl_set_list *isl_set_list_concat(
2462 __isl_take isl_set_list *list1,
2463 __isl_take isl_set_list *list2);
2464 void *isl_set_list_free(__isl_take isl_set_list *list);
2466 C<isl_set_list_alloc> creates an empty list with a capacity for
2467 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2470 Lists can be inspected using the following functions.
2472 #include <isl/list.h>
2473 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2474 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2475 __isl_give isl_set *isl_set_list_get_set(
2476 __isl_keep isl_set_list *list, int index);
2477 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2478 int (*fn)(__isl_take isl_set *el, void *user),
2481 Lists can be printed using
2483 #include <isl/list.h>
2484 __isl_give isl_printer *isl_printer_print_set_list(
2485 __isl_take isl_printer *p,
2486 __isl_keep isl_set_list *list);
2490 Matrices can be created, copied and freed using the following functions.
2492 #include <isl/mat.h>
2493 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2494 unsigned n_row, unsigned n_col);
2495 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2496 void isl_mat_free(__isl_take isl_mat *mat);
2498 Note that the elements of a newly created matrix may have arbitrary values.
2499 The elements can be changed and inspected using the following functions.
2501 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2502 int isl_mat_rows(__isl_keep isl_mat *mat);
2503 int isl_mat_cols(__isl_keep isl_mat *mat);
2504 int isl_mat_get_element(__isl_keep isl_mat *mat,
2505 int row, int col, isl_int *v);
2506 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2507 int row, int col, isl_int v);
2508 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2509 int row, int col, int v);
2511 C<isl_mat_get_element> will return a negative value if anything went wrong.
2512 In that case, the value of C<*v> is undefined.
2514 The following function can be used to compute the (right) inverse
2515 of a matrix, i.e., a matrix such that the product of the original
2516 and the inverse (in that order) is a multiple of the identity matrix.
2517 The input matrix is assumed to be of full row-rank.
2519 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2521 The following function can be used to compute the (right) kernel
2522 (or null space) of a matrix, i.e., a matrix such that the product of
2523 the original and the kernel (in that order) is the zero matrix.
2525 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2527 =head2 Piecewise Quasi Affine Expressions
2529 The zero quasi affine expression on a given domain can be created using
2531 __isl_give isl_aff *isl_aff_zero_on_domain(
2532 __isl_take isl_local_space *ls);
2534 Note that the space in which the resulting object lives is a map space
2535 with the given space as domain and a one-dimensional range.
2537 An empty piecewise quasi affine expression (one with no cells)
2538 or a piecewise quasi affine expression with a single cell can
2539 be created using the following functions.
2541 #include <isl/aff.h>
2542 __isl_give isl_pw_aff *isl_pw_aff_empty(
2543 __isl_take isl_space *space);
2544 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2545 __isl_take isl_set *set, __isl_take isl_aff *aff);
2546 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2547 __isl_take isl_aff *aff);
2549 Quasi affine expressions can be copied and freed using
2551 #include <isl/aff.h>
2552 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2553 void *isl_aff_free(__isl_take isl_aff *aff);
2555 __isl_give isl_pw_aff *isl_pw_aff_copy(
2556 __isl_keep isl_pw_aff *pwaff);
2557 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2559 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2560 using the following function. The constraint is required to have
2561 a non-zero coefficient for the specified dimension.
2563 #include <isl/constraint.h>
2564 __isl_give isl_aff *isl_constraint_get_bound(
2565 __isl_keep isl_constraint *constraint,
2566 enum isl_dim_type type, int pos);
2568 The entire affine expression of the constraint can also be extracted
2569 using the following function.
2571 #include <isl/constraint.h>
2572 __isl_give isl_aff *isl_constraint_get_aff(
2573 __isl_keep isl_constraint *constraint);
2575 Conversely, an equality constraint equating
2576 the affine expression to zero or an inequality constraint enforcing
2577 the affine expression to be non-negative, can be constructed using
2579 __isl_give isl_constraint *isl_equality_from_aff(
2580 __isl_take isl_aff *aff);
2581 __isl_give isl_constraint *isl_inequality_from_aff(
2582 __isl_take isl_aff *aff);
2584 The expression can be inspected using
2586 #include <isl/aff.h>
2587 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2588 int isl_aff_dim(__isl_keep isl_aff *aff,
2589 enum isl_dim_type type);
2590 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2591 __isl_keep isl_aff *aff);
2592 __isl_give isl_local_space *isl_aff_get_local_space(
2593 __isl_keep isl_aff *aff);
2594 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2595 enum isl_dim_type type, unsigned pos);
2596 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2598 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2599 enum isl_dim_type type, int pos, isl_int *v);
2600 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2602 __isl_give isl_aff *isl_aff_get_div(
2603 __isl_keep isl_aff *aff, int pos);
2605 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2606 int (*fn)(__isl_take isl_set *set,
2607 __isl_take isl_aff *aff,
2608 void *user), void *user);
2610 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2611 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2613 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2614 enum isl_dim_type type, unsigned first, unsigned n);
2615 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2616 enum isl_dim_type type, unsigned first, unsigned n);
2618 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2619 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2620 enum isl_dim_type type);
2621 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2623 It can be modified using
2625 #include <isl/aff.h>
2626 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2627 __isl_take isl_pw_aff *pwaff,
2628 enum isl_dim_type type, __isl_take isl_id *id);
2629 __isl_give isl_aff *isl_aff_set_dim_name(
2630 __isl_take isl_aff *aff, enum isl_dim_type type,
2631 unsigned pos, const char *s);
2632 __isl_give isl_aff *isl_aff_set_constant(
2633 __isl_take isl_aff *aff, isl_int v);
2634 __isl_give isl_aff *isl_aff_set_constant_si(
2635 __isl_take isl_aff *aff, int v);
2636 __isl_give isl_aff *isl_aff_set_coefficient(
2637 __isl_take isl_aff *aff,
2638 enum isl_dim_type type, int pos, isl_int v);
2639 __isl_give isl_aff *isl_aff_set_coefficient_si(
2640 __isl_take isl_aff *aff,
2641 enum isl_dim_type type, int pos, int v);
2642 __isl_give isl_aff *isl_aff_set_denominator(
2643 __isl_take isl_aff *aff, isl_int v);
2645 __isl_give isl_aff *isl_aff_add_constant(
2646 __isl_take isl_aff *aff, isl_int v);
2647 __isl_give isl_aff *isl_aff_add_constant_si(
2648 __isl_take isl_aff *aff, int v);
2649 __isl_give isl_aff *isl_aff_add_coefficient(
2650 __isl_take isl_aff *aff,
2651 enum isl_dim_type type, int pos, isl_int v);
2652 __isl_give isl_aff *isl_aff_add_coefficient_si(
2653 __isl_take isl_aff *aff,
2654 enum isl_dim_type type, int pos, int v);
2656 __isl_give isl_aff *isl_aff_insert_dims(
2657 __isl_take isl_aff *aff,
2658 enum isl_dim_type type, unsigned first, unsigned n);
2659 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2660 __isl_take isl_pw_aff *pwaff,
2661 enum isl_dim_type type, unsigned first, unsigned n);
2662 __isl_give isl_aff *isl_aff_add_dims(
2663 __isl_take isl_aff *aff,
2664 enum isl_dim_type type, unsigned n);
2665 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2666 __isl_take isl_pw_aff *pwaff,
2667 enum isl_dim_type type, unsigned n);
2668 __isl_give isl_aff *isl_aff_drop_dims(
2669 __isl_take isl_aff *aff,
2670 enum isl_dim_type type, unsigned first, unsigned n);
2671 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2672 __isl_take isl_pw_aff *pwaff,
2673 enum isl_dim_type type, unsigned first, unsigned n);
2675 Note that the C<set_constant> and C<set_coefficient> functions
2676 set the I<numerator> of the constant or coefficient, while
2677 C<add_constant> and C<add_coefficient> add an integer value to
2678 the possibly rational constant or coefficient.
2680 To check whether an affine expressions is obviously zero
2681 or obviously equal to some other affine expression, use
2683 #include <isl/aff.h>
2684 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2685 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2686 __isl_keep isl_aff *aff2);
2687 int isl_pw_aff_plain_is_equal(
2688 __isl_keep isl_pw_aff *pwaff1,
2689 __isl_keep isl_pw_aff *pwaff2);
2693 #include <isl/aff.h>
2694 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2695 __isl_take isl_aff *aff2);
2696 __isl_give isl_pw_aff *isl_pw_aff_add(
2697 __isl_take isl_pw_aff *pwaff1,
2698 __isl_take isl_pw_aff *pwaff2);
2699 __isl_give isl_pw_aff *isl_pw_aff_min(
2700 __isl_take isl_pw_aff *pwaff1,
2701 __isl_take isl_pw_aff *pwaff2);
2702 __isl_give isl_pw_aff *isl_pw_aff_max(
2703 __isl_take isl_pw_aff *pwaff1,
2704 __isl_take isl_pw_aff *pwaff2);
2705 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2706 __isl_take isl_aff *aff2);
2707 __isl_give isl_pw_aff *isl_pw_aff_sub(
2708 __isl_take isl_pw_aff *pwaff1,
2709 __isl_take isl_pw_aff *pwaff2);
2710 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2711 __isl_give isl_pw_aff *isl_pw_aff_neg(
2712 __isl_take isl_pw_aff *pwaff);
2713 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2714 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2715 __isl_take isl_pw_aff *pwaff);
2716 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2717 __isl_give isl_pw_aff *isl_pw_aff_floor(
2718 __isl_take isl_pw_aff *pwaff);
2719 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2721 __isl_give isl_pw_aff *isl_pw_aff_mod(
2722 __isl_take isl_pw_aff *pwaff, isl_int mod);
2723 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2725 __isl_give isl_pw_aff *isl_pw_aff_scale(
2726 __isl_take isl_pw_aff *pwaff, isl_int f);
2727 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2729 __isl_give isl_aff *isl_aff_scale_down_ui(
2730 __isl_take isl_aff *aff, unsigned f);
2731 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2732 __isl_take isl_pw_aff *pwaff, isl_int f);
2734 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2735 __isl_take isl_pw_aff_list *list);
2736 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2737 __isl_take isl_pw_aff_list *list);
2739 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2740 __isl_take isl_pw_aff *pwqp);
2742 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2743 __isl_take isl_pw_aff *pwaff,
2744 __isl_take isl_space *model);
2746 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2747 __isl_take isl_set *context);
2748 __isl_give isl_pw_aff *isl_pw_aff_gist(
2749 __isl_take isl_pw_aff *pwaff,
2750 __isl_take isl_set *context);
2752 __isl_give isl_set *isl_pw_aff_domain(
2753 __isl_take isl_pw_aff *pwaff);
2754 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2755 __isl_take isl_pw_aff *pa,
2756 __isl_take isl_set *set);
2758 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2759 __isl_take isl_aff *aff2);
2760 __isl_give isl_pw_aff *isl_pw_aff_mul(
2761 __isl_take isl_pw_aff *pwaff1,
2762 __isl_take isl_pw_aff *pwaff2);
2764 When multiplying two affine expressions, at least one of the two needs
2767 #include <isl/aff.h>
2768 __isl_give isl_basic_set *isl_aff_le_basic_set(
2769 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2770 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2771 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2772 __isl_give isl_set *isl_pw_aff_eq_set(
2773 __isl_take isl_pw_aff *pwaff1,
2774 __isl_take isl_pw_aff *pwaff2);
2775 __isl_give isl_set *isl_pw_aff_ne_set(
2776 __isl_take isl_pw_aff *pwaff1,
2777 __isl_take isl_pw_aff *pwaff2);
2778 __isl_give isl_set *isl_pw_aff_le_set(
2779 __isl_take isl_pw_aff *pwaff1,
2780 __isl_take isl_pw_aff *pwaff2);
2781 __isl_give isl_set *isl_pw_aff_lt_set(
2782 __isl_take isl_pw_aff *pwaff1,
2783 __isl_take isl_pw_aff *pwaff2);
2784 __isl_give isl_set *isl_pw_aff_ge_set(
2785 __isl_take isl_pw_aff *pwaff1,
2786 __isl_take isl_pw_aff *pwaff2);
2787 __isl_give isl_set *isl_pw_aff_gt_set(
2788 __isl_take isl_pw_aff *pwaff1,
2789 __isl_take isl_pw_aff *pwaff2);
2791 __isl_give isl_set *isl_pw_aff_list_eq_set(
2792 __isl_take isl_pw_aff_list *list1,
2793 __isl_take isl_pw_aff_list *list2);
2794 __isl_give isl_set *isl_pw_aff_list_ne_set(
2795 __isl_take isl_pw_aff_list *list1,
2796 __isl_take isl_pw_aff_list *list2);
2797 __isl_give isl_set *isl_pw_aff_list_le_set(
2798 __isl_take isl_pw_aff_list *list1,
2799 __isl_take isl_pw_aff_list *list2);
2800 __isl_give isl_set *isl_pw_aff_list_lt_set(
2801 __isl_take isl_pw_aff_list *list1,
2802 __isl_take isl_pw_aff_list *list2);
2803 __isl_give isl_set *isl_pw_aff_list_ge_set(
2804 __isl_take isl_pw_aff_list *list1,
2805 __isl_take isl_pw_aff_list *list2);
2806 __isl_give isl_set *isl_pw_aff_list_gt_set(
2807 __isl_take isl_pw_aff_list *list1,
2808 __isl_take isl_pw_aff_list *list2);
2810 The function C<isl_aff_ge_basic_set> returns a basic set
2811 containing those elements in the shared space
2812 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2813 The function C<isl_aff_ge_set> returns a set
2814 containing those elements in the shared domain
2815 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2816 The functions operating on C<isl_pw_aff_list> apply the corresponding
2817 C<isl_pw_aff> function to each pair of elements in the two lists.
2819 #include <isl/aff.h>
2820 __isl_give isl_set *isl_pw_aff_nonneg_set(
2821 __isl_take isl_pw_aff *pwaff);
2822 __isl_give isl_set *isl_pw_aff_zero_set(
2823 __isl_take isl_pw_aff *pwaff);
2824 __isl_give isl_set *isl_pw_aff_non_zero_set(
2825 __isl_take isl_pw_aff *pwaff);
2827 The function C<isl_pw_aff_nonneg_set> returns a set
2828 containing those elements in the domain
2829 of C<pwaff> where C<pwaff> is non-negative.
2831 #include <isl/aff.h>
2832 __isl_give isl_pw_aff *isl_pw_aff_cond(
2833 __isl_take isl_set *cond,
2834 __isl_take isl_pw_aff *pwaff_true,
2835 __isl_take isl_pw_aff *pwaff_false);
2837 The function C<isl_pw_aff_cond> performs a conditional operator
2838 and returns an expression that is equal to C<pwaff_true>
2839 for elements in C<cond> and equal to C<pwaff_false> for elements
2842 #include <isl/aff.h>
2843 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2844 __isl_take isl_pw_aff *pwaff1,
2845 __isl_take isl_pw_aff *pwaff2);
2846 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2847 __isl_take isl_pw_aff *pwaff1,
2848 __isl_take isl_pw_aff *pwaff2);
2850 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2851 expression with a domain that is the union of those of C<pwaff1> and
2852 C<pwaff2> and such that on each cell, the quasi-affine expression is
2853 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2854 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2855 associated expression is the defined one.
2857 An expression can be printed using
2859 #include <isl/aff.h>
2860 __isl_give isl_printer *isl_printer_print_aff(
2861 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2863 __isl_give isl_printer *isl_printer_print_pw_aff(
2864 __isl_take isl_printer *p,
2865 __isl_keep isl_pw_aff *pwaff);
2869 Points are elements of a set. They can be used to construct
2870 simple sets (boxes) or they can be used to represent the
2871 individual elements of a set.
2872 The zero point (the origin) can be created using
2874 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2876 The coordinates of a point can be inspected, set and changed
2879 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2880 enum isl_dim_type type, int pos, isl_int *v);
2881 __isl_give isl_point *isl_point_set_coordinate(
2882 __isl_take isl_point *pnt,
2883 enum isl_dim_type type, int pos, isl_int v);
2885 __isl_give isl_point *isl_point_add_ui(
2886 __isl_take isl_point *pnt,
2887 enum isl_dim_type type, int pos, unsigned val);
2888 __isl_give isl_point *isl_point_sub_ui(
2889 __isl_take isl_point *pnt,
2890 enum isl_dim_type type, int pos, unsigned val);
2892 Other properties can be obtained using
2894 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2896 Points can be copied or freed using
2898 __isl_give isl_point *isl_point_copy(
2899 __isl_keep isl_point *pnt);
2900 void isl_point_free(__isl_take isl_point *pnt);
2902 A singleton set can be created from a point using
2904 __isl_give isl_basic_set *isl_basic_set_from_point(
2905 __isl_take isl_point *pnt);
2906 __isl_give isl_set *isl_set_from_point(
2907 __isl_take isl_point *pnt);
2909 and a box can be created from two opposite extremal points using
2911 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2912 __isl_take isl_point *pnt1,
2913 __isl_take isl_point *pnt2);
2914 __isl_give isl_set *isl_set_box_from_points(
2915 __isl_take isl_point *pnt1,
2916 __isl_take isl_point *pnt2);
2918 All elements of a B<bounded> (union) set can be enumerated using
2919 the following functions.
2921 int isl_set_foreach_point(__isl_keep isl_set *set,
2922 int (*fn)(__isl_take isl_point *pnt, void *user),
2924 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2925 int (*fn)(__isl_take isl_point *pnt, void *user),
2928 The function C<fn> is called for each integer point in
2929 C<set> with as second argument the last argument of
2930 the C<isl_set_foreach_point> call. The function C<fn>
2931 should return C<0> on success and C<-1> on failure.
2932 In the latter case, C<isl_set_foreach_point> will stop
2933 enumerating and return C<-1> as well.
2934 If the enumeration is performed successfully and to completion,
2935 then C<isl_set_foreach_point> returns C<0>.
2937 To obtain a single point of a (basic) set, use
2939 __isl_give isl_point *isl_basic_set_sample_point(
2940 __isl_take isl_basic_set *bset);
2941 __isl_give isl_point *isl_set_sample_point(
2942 __isl_take isl_set *set);
2944 If C<set> does not contain any (integer) points, then the
2945 resulting point will be ``void'', a property that can be
2948 int isl_point_is_void(__isl_keep isl_point *pnt);
2950 =head2 Piecewise Quasipolynomials
2952 A piecewise quasipolynomial is a particular kind of function that maps
2953 a parametric point to a rational value.
2954 More specifically, a quasipolynomial is a polynomial expression in greatest
2955 integer parts of affine expressions of parameters and variables.
2956 A piecewise quasipolynomial is a subdivision of a given parametric
2957 domain into disjoint cells with a quasipolynomial associated to
2958 each cell. The value of the piecewise quasipolynomial at a given
2959 point is the value of the quasipolynomial associated to the cell
2960 that contains the point. Outside of the union of cells,
2961 the value is assumed to be zero.
2962 For example, the piecewise quasipolynomial
2964 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2966 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2967 A given piecewise quasipolynomial has a fixed domain dimension.
2968 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2969 defined over different domains.
2970 Piecewise quasipolynomials are mainly used by the C<barvinok>
2971 library for representing the number of elements in a parametric set or map.
2972 For example, the piecewise quasipolynomial above represents
2973 the number of points in the map
2975 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2977 =head3 Printing (Piecewise) Quasipolynomials
2979 Quasipolynomials and piecewise quasipolynomials can be printed
2980 using the following functions.
2982 __isl_give isl_printer *isl_printer_print_qpolynomial(
2983 __isl_take isl_printer *p,
2984 __isl_keep isl_qpolynomial *qp);
2986 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2987 __isl_take isl_printer *p,
2988 __isl_keep isl_pw_qpolynomial *pwqp);
2990 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2991 __isl_take isl_printer *p,
2992 __isl_keep isl_union_pw_qpolynomial *upwqp);
2994 The output format of the printer
2995 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2996 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2998 In case of printing in C<ISL_FORMAT_C>, the user may want
2999 to set the names of all dimensions
3001 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3002 __isl_take isl_qpolynomial *qp,
3003 enum isl_dim_type type, unsigned pos,
3005 __isl_give isl_pw_qpolynomial *
3006 isl_pw_qpolynomial_set_dim_name(
3007 __isl_take isl_pw_qpolynomial *pwqp,
3008 enum isl_dim_type type, unsigned pos,
3011 =head3 Creating New (Piecewise) Quasipolynomials
3013 Some simple quasipolynomials can be created using the following functions.
3014 More complicated quasipolynomials can be created by applying
3015 operations such as addition and multiplication
3016 on the resulting quasipolynomials
3018 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3019 __isl_take isl_space *domain);
3020 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3021 __isl_take isl_space *domain);
3022 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3023 __isl_take isl_space *domain);
3024 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3025 __isl_take isl_space *domain);
3026 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3027 __isl_take isl_space *domain);
3028 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3029 __isl_take isl_space *domain,
3030 const isl_int n, const isl_int d);
3031 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3032 __isl_take isl_space *domain,
3033 enum isl_dim_type type, unsigned pos);
3034 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3035 __isl_take isl_aff *aff);
3037 Note that the space in which a quasipolynomial lives is a map space
3038 with a one-dimensional range. The C<domain> argument in some of
3039 the functions above corresponds to the domain of this map space.
3041 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3042 with a single cell can be created using the following functions.
3043 Multiple of these single cell piecewise quasipolynomials can
3044 be combined to create more complicated piecewise quasipolynomials.
3046 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3047 __isl_take isl_space *space);
3048 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3049 __isl_take isl_set *set,
3050 __isl_take isl_qpolynomial *qp);
3051 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3052 __isl_take isl_qpolynomial *qp);
3053 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3054 __isl_take isl_pw_aff *pwaff);
3056 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3057 __isl_take isl_space *space);
3058 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3059 __isl_take isl_pw_qpolynomial *pwqp);
3060 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3061 __isl_take isl_union_pw_qpolynomial *upwqp,
3062 __isl_take isl_pw_qpolynomial *pwqp);
3064 Quasipolynomials can be copied and freed again using the following
3067 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3068 __isl_keep isl_qpolynomial *qp);
3069 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3071 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3072 __isl_keep isl_pw_qpolynomial *pwqp);
3073 void *isl_pw_qpolynomial_free(
3074 __isl_take isl_pw_qpolynomial *pwqp);
3076 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3077 __isl_keep isl_union_pw_qpolynomial *upwqp);
3078 void isl_union_pw_qpolynomial_free(
3079 __isl_take isl_union_pw_qpolynomial *upwqp);
3081 =head3 Inspecting (Piecewise) Quasipolynomials
3083 To iterate over all piecewise quasipolynomials in a union
3084 piecewise quasipolynomial, use the following function
3086 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3087 __isl_keep isl_union_pw_qpolynomial *upwqp,
3088 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3091 To extract the piecewise quasipolynomial in a given space from a union, use
3093 __isl_give isl_pw_qpolynomial *
3094 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3095 __isl_keep isl_union_pw_qpolynomial *upwqp,
3096 __isl_take isl_space *space);
3098 To iterate over the cells in a piecewise quasipolynomial,
3099 use either of the following two functions
3101 int isl_pw_qpolynomial_foreach_piece(
3102 __isl_keep isl_pw_qpolynomial *pwqp,
3103 int (*fn)(__isl_take isl_set *set,
3104 __isl_take isl_qpolynomial *qp,
3105 void *user), void *user);
3106 int isl_pw_qpolynomial_foreach_lifted_piece(
3107 __isl_keep isl_pw_qpolynomial *pwqp,
3108 int (*fn)(__isl_take isl_set *set,
3109 __isl_take isl_qpolynomial *qp,
3110 void *user), void *user);
3112 As usual, the function C<fn> should return C<0> on success
3113 and C<-1> on failure. The difference between
3114 C<isl_pw_qpolynomial_foreach_piece> and
3115 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3116 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3117 compute unique representations for all existentially quantified
3118 variables and then turn these existentially quantified variables
3119 into extra set variables, adapting the associated quasipolynomial
3120 accordingly. This means that the C<set> passed to C<fn>
3121 will not have any existentially quantified variables, but that
3122 the dimensions of the sets may be different for different
3123 invocations of C<fn>.
3125 To iterate over all terms in a quasipolynomial,
3128 int isl_qpolynomial_foreach_term(
3129 __isl_keep isl_qpolynomial *qp,
3130 int (*fn)(__isl_take isl_term *term,
3131 void *user), void *user);
3133 The terms themselves can be inspected and freed using
3136 unsigned isl_term_dim(__isl_keep isl_term *term,
3137 enum isl_dim_type type);
3138 void isl_term_get_num(__isl_keep isl_term *term,
3140 void isl_term_get_den(__isl_keep isl_term *term,
3142 int isl_term_get_exp(__isl_keep isl_term *term,
3143 enum isl_dim_type type, unsigned pos);
3144 __isl_give isl_aff *isl_term_get_div(
3145 __isl_keep isl_term *term, unsigned pos);
3146 void isl_term_free(__isl_take isl_term *term);
3148 Each term is a product of parameters, set variables and
3149 integer divisions. The function C<isl_term_get_exp>
3150 returns the exponent of a given dimensions in the given term.
3151 The C<isl_int>s in the arguments of C<isl_term_get_num>
3152 and C<isl_term_get_den> need to have been initialized
3153 using C<isl_int_init> before calling these functions.
3155 =head3 Properties of (Piecewise) Quasipolynomials
3157 To check whether a quasipolynomial is actually a constant,
3158 use the following function.
3160 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3161 isl_int *n, isl_int *d);
3163 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3164 then the numerator and denominator of the constant
3165 are returned in C<*n> and C<*d>, respectively.
3167 To check whether two union piecewise quasipolynomials are
3168 obviously equal, use
3170 int isl_union_pw_qpolynomial_plain_is_equal(
3171 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3172 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3174 =head3 Operations on (Piecewise) Quasipolynomials
3176 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3177 __isl_take isl_qpolynomial *qp, isl_int v);
3178 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3179 __isl_take isl_qpolynomial *qp);
3180 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3181 __isl_take isl_qpolynomial *qp1,
3182 __isl_take isl_qpolynomial *qp2);
3183 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3184 __isl_take isl_qpolynomial *qp1,
3185 __isl_take isl_qpolynomial *qp2);
3186 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3187 __isl_take isl_qpolynomial *qp1,
3188 __isl_take isl_qpolynomial *qp2);
3189 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3190 __isl_take isl_qpolynomial *qp, unsigned exponent);
3192 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3193 __isl_take isl_pw_qpolynomial *pwqp1,
3194 __isl_take isl_pw_qpolynomial *pwqp2);
3195 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3196 __isl_take isl_pw_qpolynomial *pwqp1,
3197 __isl_take isl_pw_qpolynomial *pwqp2);
3198 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3199 __isl_take isl_pw_qpolynomial *pwqp1,
3200 __isl_take isl_pw_qpolynomial *pwqp2);
3201 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3202 __isl_take isl_pw_qpolynomial *pwqp);
3203 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3204 __isl_take isl_pw_qpolynomial *pwqp1,
3205 __isl_take isl_pw_qpolynomial *pwqp2);
3206 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3207 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3209 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3210 __isl_take isl_union_pw_qpolynomial *upwqp1,
3211 __isl_take isl_union_pw_qpolynomial *upwqp2);
3212 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3213 __isl_take isl_union_pw_qpolynomial *upwqp1,
3214 __isl_take isl_union_pw_qpolynomial *upwqp2);
3215 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3216 __isl_take isl_union_pw_qpolynomial *upwqp1,
3217 __isl_take isl_union_pw_qpolynomial *upwqp2);
3219 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3220 __isl_take isl_pw_qpolynomial *pwqp,
3221 __isl_take isl_point *pnt);
3223 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3224 __isl_take isl_union_pw_qpolynomial *upwqp,
3225 __isl_take isl_point *pnt);
3227 __isl_give isl_set *isl_pw_qpolynomial_domain(
3228 __isl_take isl_pw_qpolynomial *pwqp);
3229 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3230 __isl_take isl_pw_qpolynomial *pwpq,
3231 __isl_take isl_set *set);
3233 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3234 __isl_take isl_union_pw_qpolynomial *upwqp);
3235 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3236 __isl_take isl_union_pw_qpolynomial *upwpq,
3237 __isl_take isl_union_set *uset);
3239 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3240 __isl_take isl_qpolynomial *qp,
3241 __isl_take isl_space *model);
3243 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3244 __isl_take isl_qpolynomial *qp);
3245 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3246 __isl_take isl_pw_qpolynomial *pwqp);
3248 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3249 __isl_take isl_union_pw_qpolynomial *upwqp);
3251 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3252 __isl_take isl_qpolynomial *qp,
3253 __isl_take isl_set *context);
3255 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3256 __isl_take isl_pw_qpolynomial *pwqp,
3257 __isl_take isl_set *context);
3259 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3260 __isl_take isl_union_pw_qpolynomial *upwqp,
3261 __isl_take isl_union_set *context);
3263 The gist operation applies the gist operation to each of
3264 the cells in the domain of the input piecewise quasipolynomial.
3265 The context is also exploited
3266 to simplify the quasipolynomials associated to each cell.
3268 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3269 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3270 __isl_give isl_union_pw_qpolynomial *
3271 isl_union_pw_qpolynomial_to_polynomial(
3272 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3274 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3275 the polynomial will be an overapproximation. If C<sign> is negative,
3276 it will be an underapproximation. If C<sign> is zero, the approximation
3277 will lie somewhere in between.
3279 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3281 A piecewise quasipolynomial reduction is a piecewise
3282 reduction (or fold) of quasipolynomials.
3283 In particular, the reduction can be maximum or a minimum.
3284 The objects are mainly used to represent the result of
3285 an upper or lower bound on a quasipolynomial over its domain,
3286 i.e., as the result of the following function.
3288 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3289 __isl_take isl_pw_qpolynomial *pwqp,
3290 enum isl_fold type, int *tight);
3292 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3293 __isl_take isl_union_pw_qpolynomial *upwqp,
3294 enum isl_fold type, int *tight);
3296 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3297 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3298 is the returned bound is known be tight, i.e., for each value
3299 of the parameters there is at least
3300 one element in the domain that reaches the bound.
3301 If the domain of C<pwqp> is not wrapping, then the bound is computed
3302 over all elements in that domain and the result has a purely parametric
3303 domain. If the domain of C<pwqp> is wrapping, then the bound is
3304 computed over the range of the wrapped relation. The domain of the
3305 wrapped relation becomes the domain of the result.
3307 A (piecewise) quasipolynomial reduction can be copied or freed using the
3308 following functions.
3310 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3311 __isl_keep isl_qpolynomial_fold *fold);
3312 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3313 __isl_keep isl_pw_qpolynomial_fold *pwf);
3314 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3315 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3316 void isl_qpolynomial_fold_free(
3317 __isl_take isl_qpolynomial_fold *fold);
3318 void *isl_pw_qpolynomial_fold_free(
3319 __isl_take isl_pw_qpolynomial_fold *pwf);
3320 void isl_union_pw_qpolynomial_fold_free(
3321 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3323 =head3 Printing Piecewise Quasipolynomial Reductions
3325 Piecewise quasipolynomial reductions can be printed
3326 using the following function.
3328 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3329 __isl_take isl_printer *p,
3330 __isl_keep isl_pw_qpolynomial_fold *pwf);
3331 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3332 __isl_take isl_printer *p,
3333 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3335 For C<isl_printer_print_pw_qpolynomial_fold>,
3336 output format of the printer
3337 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3338 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3339 output format of the printer
3340 needs to be set to C<ISL_FORMAT_ISL>.
3341 In case of printing in C<ISL_FORMAT_C>, the user may want
3342 to set the names of all dimensions
3344 __isl_give isl_pw_qpolynomial_fold *
3345 isl_pw_qpolynomial_fold_set_dim_name(
3346 __isl_take isl_pw_qpolynomial_fold *pwf,
3347 enum isl_dim_type type, unsigned pos,
3350 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3352 To iterate over all piecewise quasipolynomial reductions in a union
3353 piecewise quasipolynomial reduction, use the following function
3355 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3356 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3357 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3358 void *user), void *user);
3360 To iterate over the cells in a piecewise quasipolynomial reduction,
3361 use either of the following two functions
3363 int isl_pw_qpolynomial_fold_foreach_piece(
3364 __isl_keep isl_pw_qpolynomial_fold *pwf,
3365 int (*fn)(__isl_take isl_set *set,
3366 __isl_take isl_qpolynomial_fold *fold,
3367 void *user), void *user);
3368 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3369 __isl_keep isl_pw_qpolynomial_fold *pwf,
3370 int (*fn)(__isl_take isl_set *set,
3371 __isl_take isl_qpolynomial_fold *fold,
3372 void *user), void *user);
3374 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3375 of the difference between these two functions.
3377 To iterate over all quasipolynomials in a reduction, use
3379 int isl_qpolynomial_fold_foreach_qpolynomial(
3380 __isl_keep isl_qpolynomial_fold *fold,
3381 int (*fn)(__isl_take isl_qpolynomial *qp,
3382 void *user), void *user);
3384 =head3 Properties of Piecewise Quasipolynomial Reductions
3386 To check whether two union piecewise quasipolynomial reductions are
3387 obviously equal, use
3389 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3390 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3391 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3393 =head3 Operations on Piecewise Quasipolynomial Reductions
3395 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3396 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3398 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3399 __isl_take isl_pw_qpolynomial_fold *pwf1,
3400 __isl_take isl_pw_qpolynomial_fold *pwf2);
3402 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3403 __isl_take isl_pw_qpolynomial_fold *pwf1,
3404 __isl_take isl_pw_qpolynomial_fold *pwf2);
3406 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3407 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3408 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3410 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3411 __isl_take isl_pw_qpolynomial_fold *pwf,
3412 __isl_take isl_point *pnt);
3414 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3415 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3416 __isl_take isl_point *pnt);
3418 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3419 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3420 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3421 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3422 __isl_take isl_union_set *uset);
3424 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3425 __isl_take isl_pw_qpolynomial_fold *pwf);
3427 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3428 __isl_take isl_pw_qpolynomial_fold *pwf);
3430 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3431 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3433 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3434 __isl_take isl_pw_qpolynomial_fold *pwf,
3435 __isl_take isl_set *context);
3437 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3438 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3439 __isl_take isl_union_set *context);
3441 The gist operation applies the gist operation to each of
3442 the cells in the domain of the input piecewise quasipolynomial reduction.
3443 In future, the operation will also exploit the context
3444 to simplify the quasipolynomial reductions associated to each cell.
3446 __isl_give isl_pw_qpolynomial_fold *
3447 isl_set_apply_pw_qpolynomial_fold(
3448 __isl_take isl_set *set,
3449 __isl_take isl_pw_qpolynomial_fold *pwf,
3451 __isl_give isl_pw_qpolynomial_fold *
3452 isl_map_apply_pw_qpolynomial_fold(
3453 __isl_take isl_map *map,
3454 __isl_take isl_pw_qpolynomial_fold *pwf,
3456 __isl_give isl_union_pw_qpolynomial_fold *
3457 isl_union_set_apply_union_pw_qpolynomial_fold(
3458 __isl_take isl_union_set *uset,
3459 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3461 __isl_give isl_union_pw_qpolynomial_fold *
3462 isl_union_map_apply_union_pw_qpolynomial_fold(
3463 __isl_take isl_union_map *umap,
3464 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3467 The functions taking a map
3468 compose the given map with the given piecewise quasipolynomial reduction.
3469 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3470 over all elements in the intersection of the range of the map
3471 and the domain of the piecewise quasipolynomial reduction
3472 as a function of an element in the domain of the map.
3473 The functions taking a set compute a bound over all elements in the
3474 intersection of the set and the domain of the
3475 piecewise quasipolynomial reduction.
3477 =head2 Dependence Analysis
3479 C<isl> contains specialized functionality for performing
3480 array dataflow analysis. That is, given a I<sink> access relation
3481 and a collection of possible I<source> access relations,
3482 C<isl> can compute relations that describe
3483 for each iteration of the sink access, which iteration
3484 of which of the source access relations was the last
3485 to access the same data element before the given iteration
3487 To compute standard flow dependences, the sink should be
3488 a read, while the sources should be writes.
3489 If any of the source accesses are marked as being I<may>
3490 accesses, then there will be a dependence to the last
3491 I<must> access B<and> to any I<may> access that follows
3492 this last I<must> access.
3493 In particular, if I<all> sources are I<may> accesses,
3494 then memory based dependence analysis is performed.
3495 If, on the other hand, all sources are I<must> accesses,
3496 then value based dependence analysis is performed.
3498 #include <isl/flow.h>
3500 typedef int (*isl_access_level_before)(void *first, void *second);
3502 __isl_give isl_access_info *isl_access_info_alloc(
3503 __isl_take isl_map *sink,
3504 void *sink_user, isl_access_level_before fn,
3506 __isl_give isl_access_info *isl_access_info_add_source(
3507 __isl_take isl_access_info *acc,
3508 __isl_take isl_map *source, int must,
3510 void isl_access_info_free(__isl_take isl_access_info *acc);
3512 __isl_give isl_flow *isl_access_info_compute_flow(
3513 __isl_take isl_access_info *acc);
3515 int isl_flow_foreach(__isl_keep isl_flow *deps,
3516 int (*fn)(__isl_take isl_map *dep, int must,
3517 void *dep_user, void *user),
3519 __isl_give isl_map *isl_flow_get_no_source(
3520 __isl_keep isl_flow *deps, int must);
3521 void isl_flow_free(__isl_take isl_flow *deps);
3523 The function C<isl_access_info_compute_flow> performs the actual
3524 dependence analysis. The other functions are used to construct
3525 the input for this function or to read off the output.
3527 The input is collected in an C<isl_access_info>, which can
3528 be created through a call to C<isl_access_info_alloc>.
3529 The arguments to this functions are the sink access relation
3530 C<sink>, a token C<sink_user> used to identify the sink
3531 access to the user, a callback function for specifying the
3532 relative order of source and sink accesses, and the number
3533 of source access relations that will be added.
3534 The callback function has type C<int (*)(void *first, void *second)>.
3535 The function is called with two user supplied tokens identifying
3536 either a source or the sink and it should return the shared nesting
3537 level and the relative order of the two accesses.
3538 In particular, let I<n> be the number of loops shared by
3539 the two accesses. If C<first> precedes C<second> textually,
3540 then the function should return I<2 * n + 1>; otherwise,
3541 it should return I<2 * n>.
3542 The sources can be added to the C<isl_access_info> by performing
3543 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3544 C<must> indicates whether the source is a I<must> access
3545 or a I<may> access. Note that a multi-valued access relation
3546 should only be marked I<must> if every iteration in the domain
3547 of the relation accesses I<all> elements in its image.
3548 The C<source_user> token is again used to identify
3549 the source access. The range of the source access relation
3550 C<source> should have the same dimension as the range
3551 of the sink access relation.
3552 The C<isl_access_info_free> function should usually not be
3553 called explicitly, because it is called implicitly by
3554 C<isl_access_info_compute_flow>.
3556 The result of the dependence analysis is collected in an
3557 C<isl_flow>. There may be elements of
3558 the sink access for which no preceding source access could be
3559 found or for which all preceding sources are I<may> accesses.
3560 The relations containing these elements can be obtained through
3561 calls to C<isl_flow_get_no_source>, the first with C<must> set
3562 and the second with C<must> unset.
3563 In the case of standard flow dependence analysis,
3564 with the sink a read and the sources I<must> writes,
3565 the first relation corresponds to the reads from uninitialized
3566 array elements and the second relation is empty.
3567 The actual flow dependences can be extracted using
3568 C<isl_flow_foreach>. This function will call the user-specified
3569 callback function C<fn> for each B<non-empty> dependence between
3570 a source and the sink. The callback function is called
3571 with four arguments, the actual flow dependence relation
3572 mapping source iterations to sink iterations, a boolean that
3573 indicates whether it is a I<must> or I<may> dependence, a token
3574 identifying the source and an additional C<void *> with value
3575 equal to the third argument of the C<isl_flow_foreach> call.
3576 A dependence is marked I<must> if it originates from a I<must>
3577 source and if it is not followed by any I<may> sources.
3579 After finishing with an C<isl_flow>, the user should call
3580 C<isl_flow_free> to free all associated memory.
3582 A higher-level interface to dependence analysis is provided
3583 by the following function.
3585 #include <isl/flow.h>
3587 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3588 __isl_take isl_union_map *must_source,
3589 __isl_take isl_union_map *may_source,
3590 __isl_take isl_union_map *schedule,
3591 __isl_give isl_union_map **must_dep,
3592 __isl_give isl_union_map **may_dep,
3593 __isl_give isl_union_map **must_no_source,
3594 __isl_give isl_union_map **may_no_source);
3596 The arrays are identified by the tuple names of the ranges
3597 of the accesses. The iteration domains by the tuple names
3598 of the domains of the accesses and of the schedule.
3599 The relative order of the iteration domains is given by the
3600 schedule. The relations returned through C<must_no_source>
3601 and C<may_no_source> are subsets of C<sink>.
3602 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3603 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3604 any of the other arguments is treated as an error.
3608 B<The functionality described in this section is fairly new
3609 and may be subject to change.>
3611 The following function can be used to compute a schedule
3612 for a union of domains. The generated schedule respects
3613 all C<validity> dependences. That is, all dependence distances
3614 over these dependences in the scheduled space are lexicographically
3615 positive. The generated schedule schedule also tries to minimize
3616 the dependence distances over C<proximity> dependences.
3617 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3618 for groups of domains where the dependence distances have only
3619 non-negative values.
3620 The algorithm used to construct the schedule is similar to that
3623 #include <isl/schedule.h>
3624 __isl_give isl_schedule *isl_union_set_compute_schedule(
3625 __isl_take isl_union_set *domain,
3626 __isl_take isl_union_map *validity,
3627 __isl_take isl_union_map *proximity);
3628 void *isl_schedule_free(__isl_take isl_schedule *sched);
3630 A mapping from the domains to the scheduled space can be obtained
3631 from an C<isl_schedule> using the following function.
3633 __isl_give isl_union_map *isl_schedule_get_map(
3634 __isl_keep isl_schedule *sched);
3636 A representation of the schedule can be printed using
3638 __isl_give isl_printer *isl_printer_print_schedule(
3639 __isl_take isl_printer *p,
3640 __isl_keep isl_schedule *schedule);
3642 A representation of the schedule as a forest of bands can be obtained
3643 using the following function.
3645 __isl_give isl_band_list *isl_schedule_get_band_forest(
3646 __isl_keep isl_schedule *schedule);
3648 The list can be manipulated as explained in L<"Lists">.
3649 The bands inside the list can be copied and freed using the following
3652 #include <isl/band.h>
3653 __isl_give isl_band *isl_band_copy(
3654 __isl_keep isl_band *band);
3655 void *isl_band_free(__isl_take isl_band *band);
3657 Each band contains zero or more scheduling dimensions.
3658 These are referred to as the members of the band.
3659 The section of the schedule that corresponds to the band is
3660 referred to as the partial schedule of the band.
3661 For those nodes that participate in a band, the outer scheduling
3662 dimensions form the prefix schedule, while the inner scheduling
3663 dimensions form the suffix schedule.
3664 That is, if we take a cut of the band forest, then the union of
3665 the concatenations of the prefix, partial and suffix schedules of
3666 each band in the cut is equal to the entire schedule (modulo
3667 some possible padding at the end with zero scheduling dimensions).
3668 The properties of a band can be inspected using the following functions.
3670 #include <isl/band.h>
3671 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3673 int isl_band_has_children(__isl_keep isl_band *band);
3674 __isl_give isl_band_list *isl_band_get_children(
3675 __isl_keep isl_band *band);
3677 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3678 __isl_keep isl_band *band);
3679 __isl_give isl_union_map *isl_band_get_partial_schedule(
3680 __isl_keep isl_band *band);
3681 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3682 __isl_keep isl_band *band);
3684 int isl_band_n_member(__isl_keep isl_band *band);
3685 int isl_band_member_is_zero_distance(
3686 __isl_keep isl_band *band, int pos);
3688 Note that a scheduling dimension is considered to be ``zero
3689 distance'' if it does not carry any proximity dependences
3691 That is, if the dependence distances of the proximity
3692 dependences are all zero in that direction (for fixed
3693 iterations of outer bands).
3695 A representation of the band can be printed using
3697 #include <isl/band.h>
3698 __isl_give isl_printer *isl_printer_print_band(
3699 __isl_take isl_printer *p,
3700 __isl_keep isl_band *band);
3702 =head2 Parametric Vertex Enumeration
3704 The parametric vertex enumeration described in this section
3705 is mainly intended to be used internally and by the C<barvinok>
3708 #include <isl/vertices.h>
3709 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3710 __isl_keep isl_basic_set *bset);
3712 The function C<isl_basic_set_compute_vertices> performs the
3713 actual computation of the parametric vertices and the chamber
3714 decomposition and store the result in an C<isl_vertices> object.
3715 This information can be queried by either iterating over all
3716 the vertices or iterating over all the chambers or cells
3717 and then iterating over all vertices that are active on the chamber.
3719 int isl_vertices_foreach_vertex(
3720 __isl_keep isl_vertices *vertices,
3721 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3724 int isl_vertices_foreach_cell(
3725 __isl_keep isl_vertices *vertices,
3726 int (*fn)(__isl_take isl_cell *cell, void *user),
3728 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3729 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3732 Other operations that can be performed on an C<isl_vertices> object are
3735 isl_ctx *isl_vertices_get_ctx(
3736 __isl_keep isl_vertices *vertices);
3737 int isl_vertices_get_n_vertices(
3738 __isl_keep isl_vertices *vertices);
3739 void isl_vertices_free(__isl_take isl_vertices *vertices);
3741 Vertices can be inspected and destroyed using the following functions.
3743 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3744 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3745 __isl_give isl_basic_set *isl_vertex_get_domain(
3746 __isl_keep isl_vertex *vertex);
3747 __isl_give isl_basic_set *isl_vertex_get_expr(
3748 __isl_keep isl_vertex *vertex);
3749 void isl_vertex_free(__isl_take isl_vertex *vertex);
3751 C<isl_vertex_get_expr> returns a singleton parametric set describing
3752 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3754 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3755 B<rational> basic sets, so they should mainly be used for inspection
3756 and should not be mixed with integer sets.
3758 Chambers can be inspected and destroyed using the following functions.
3760 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3761 __isl_give isl_basic_set *isl_cell_get_domain(
3762 __isl_keep isl_cell *cell);
3763 void isl_cell_free(__isl_take isl_cell *cell);
3767 Although C<isl> is mainly meant to be used as a library,
3768 it also contains some basic applications that use some
3769 of the functionality of C<isl>.
3770 The input may be specified in either the L<isl format>
3771 or the L<PolyLib format>.
3773 =head2 C<isl_polyhedron_sample>
3775 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3776 an integer element of the polyhedron, if there is any.
3777 The first column in the output is the denominator and is always
3778 equal to 1. If the polyhedron contains no integer points,
3779 then a vector of length zero is printed.
3783 C<isl_pip> takes the same input as the C<example> program
3784 from the C<piplib> distribution, i.e., a set of constraints
3785 on the parameters, a line containing only -1 and finally a set
3786 of constraints on a parametric polyhedron.
3787 The coefficients of the parameters appear in the last columns
3788 (but before the final constant column).
3789 The output is the lexicographic minimum of the parametric polyhedron.
3790 As C<isl> currently does not have its own output format, the output
3791 is just a dump of the internal state.
3793 =head2 C<isl_polyhedron_minimize>
3795 C<isl_polyhedron_minimize> computes the minimum of some linear
3796 or affine objective function over the integer points in a polyhedron.
3797 If an affine objective function
3798 is given, then the constant should appear in the last column.
3800 =head2 C<isl_polytope_scan>
3802 Given a polytope, C<isl_polytope_scan> prints
3803 all integer points in the polytope.