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 int isl_basic_map_has_dim_id(
1471 __isl_keep isl_basic_map *bmap,
1472 enum isl_dim_type type, unsigned pos);
1473 __isl_give isl_map *isl_map_set_dim_id(
1474 __isl_take isl_map *map, enum isl_dim_type type,
1475 unsigned pos, __isl_take isl_id *id);
1476 int isl_map_has_dim_id(__isl_keep isl_map *map,
1477 enum isl_dim_type type, unsigned pos);
1478 __isl_give isl_id *isl_map_get_dim_id(
1479 __isl_keep isl_map *map, enum isl_dim_type type,
1482 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1483 enum isl_dim_type type, __isl_keep isl_id *id);
1484 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1485 enum isl_dim_type type, __isl_keep isl_id *id);
1486 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1487 enum isl_dim_type type, const char *name);
1489 const char *isl_constraint_get_dim_name(
1490 __isl_keep isl_constraint *constraint,
1491 enum isl_dim_type type, unsigned pos);
1492 const char *isl_basic_set_get_dim_name(
1493 __isl_keep isl_basic_set *bset,
1494 enum isl_dim_type type, unsigned pos);
1495 const char *isl_set_get_dim_name(
1496 __isl_keep isl_set *set,
1497 enum isl_dim_type type, unsigned pos);
1498 const char *isl_basic_map_get_dim_name(
1499 __isl_keep isl_basic_map *bmap,
1500 enum isl_dim_type type, unsigned pos);
1501 const char *isl_map_get_dim_name(
1502 __isl_keep isl_map *map,
1503 enum isl_dim_type type, unsigned pos);
1505 These functions are mostly useful to obtain the identifiers, positions
1506 or names of the parameters. Identifiers of individual dimensions are
1507 essentially only useful for printing. They are ignored by all other
1508 operations and may not be preserved across those operations.
1512 =head3 Unary Properties
1518 The following functions test whether the given set or relation
1519 contains any integer points. The ``plain'' variants do not perform
1520 any computations, but simply check if the given set or relation
1521 is already known to be empty.
1523 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1524 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1525 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1526 int isl_set_is_empty(__isl_keep isl_set *set);
1527 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1528 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1529 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1530 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1531 int isl_map_is_empty(__isl_keep isl_map *map);
1532 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1534 =item * Universality
1536 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1537 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1538 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1540 =item * Single-valuedness
1542 int isl_map_is_single_valued(__isl_keep isl_map *map);
1543 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1547 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1548 int isl_map_is_injective(__isl_keep isl_map *map);
1549 int isl_union_map_plain_is_injective(
1550 __isl_keep isl_union_map *umap);
1551 int isl_union_map_is_injective(
1552 __isl_keep isl_union_map *umap);
1556 int isl_map_is_bijective(__isl_keep isl_map *map);
1557 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1561 int isl_basic_map_plain_is_fixed(
1562 __isl_keep isl_basic_map *bmap,
1563 enum isl_dim_type type, unsigned pos,
1565 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1566 enum isl_dim_type type, unsigned pos,
1568 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1569 enum isl_dim_type type, unsigned pos,
1572 Check if the relation obviously lies on a hyperplane where the given dimension
1573 has a fixed value and if so, return that value in C<*val>.
1577 To check whether a set is a parameter domain, use this function:
1579 int isl_set_is_params(__isl_keep isl_set *set);
1583 The following functions check whether the domain of the given
1584 (basic) set is a wrapped relation.
1586 int isl_basic_set_is_wrapping(
1587 __isl_keep isl_basic_set *bset);
1588 int isl_set_is_wrapping(__isl_keep isl_set *set);
1590 =item * Internal Product
1592 int isl_basic_map_can_zip(
1593 __isl_keep isl_basic_map *bmap);
1594 int isl_map_can_zip(__isl_keep isl_map *map);
1596 Check whether the product of domain and range of the given relation
1598 i.e., whether both domain and range are nested relations.
1602 =head3 Binary Properties
1608 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1609 __isl_keep isl_set *set2);
1610 int isl_set_is_equal(__isl_keep isl_set *set1,
1611 __isl_keep isl_set *set2);
1612 int isl_union_set_is_equal(
1613 __isl_keep isl_union_set *uset1,
1614 __isl_keep isl_union_set *uset2);
1615 int isl_basic_map_is_equal(
1616 __isl_keep isl_basic_map *bmap1,
1617 __isl_keep isl_basic_map *bmap2);
1618 int isl_map_is_equal(__isl_keep isl_map *map1,
1619 __isl_keep isl_map *map2);
1620 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1621 __isl_keep isl_map *map2);
1622 int isl_union_map_is_equal(
1623 __isl_keep isl_union_map *umap1,
1624 __isl_keep isl_union_map *umap2);
1626 =item * Disjointness
1628 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1629 __isl_keep isl_set *set2);
1633 int isl_set_is_subset(__isl_keep isl_set *set1,
1634 __isl_keep isl_set *set2);
1635 int isl_set_is_strict_subset(
1636 __isl_keep isl_set *set1,
1637 __isl_keep isl_set *set2);
1638 int isl_union_set_is_subset(
1639 __isl_keep isl_union_set *uset1,
1640 __isl_keep isl_union_set *uset2);
1641 int isl_union_set_is_strict_subset(
1642 __isl_keep isl_union_set *uset1,
1643 __isl_keep isl_union_set *uset2);
1644 int isl_basic_map_is_subset(
1645 __isl_keep isl_basic_map *bmap1,
1646 __isl_keep isl_basic_map *bmap2);
1647 int isl_basic_map_is_strict_subset(
1648 __isl_keep isl_basic_map *bmap1,
1649 __isl_keep isl_basic_map *bmap2);
1650 int isl_map_is_subset(
1651 __isl_keep isl_map *map1,
1652 __isl_keep isl_map *map2);
1653 int isl_map_is_strict_subset(
1654 __isl_keep isl_map *map1,
1655 __isl_keep isl_map *map2);
1656 int isl_union_map_is_subset(
1657 __isl_keep isl_union_map *umap1,
1658 __isl_keep isl_union_map *umap2);
1659 int isl_union_map_is_strict_subset(
1660 __isl_keep isl_union_map *umap1,
1661 __isl_keep isl_union_map *umap2);
1665 =head2 Unary Operations
1671 __isl_give isl_set *isl_set_complement(
1672 __isl_take isl_set *set);
1676 __isl_give isl_basic_map *isl_basic_map_reverse(
1677 __isl_take isl_basic_map *bmap);
1678 __isl_give isl_map *isl_map_reverse(
1679 __isl_take isl_map *map);
1680 __isl_give isl_union_map *isl_union_map_reverse(
1681 __isl_take isl_union_map *umap);
1685 __isl_give isl_basic_set *isl_basic_set_project_out(
1686 __isl_take isl_basic_set *bset,
1687 enum isl_dim_type type, unsigned first, unsigned n);
1688 __isl_give isl_basic_map *isl_basic_map_project_out(
1689 __isl_take isl_basic_map *bmap,
1690 enum isl_dim_type type, unsigned first, unsigned n);
1691 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1692 enum isl_dim_type type, unsigned first, unsigned n);
1693 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1694 enum isl_dim_type type, unsigned first, unsigned n);
1695 __isl_give isl_basic_set *isl_basic_set_params(
1696 __isl_take isl_basic_set *bset);
1697 __isl_give isl_basic_set *isl_basic_map_domain(
1698 __isl_take isl_basic_map *bmap);
1699 __isl_give isl_basic_set *isl_basic_map_range(
1700 __isl_take isl_basic_map *bmap);
1701 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1702 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1703 __isl_give isl_set *isl_map_domain(
1704 __isl_take isl_map *bmap);
1705 __isl_give isl_set *isl_map_range(
1706 __isl_take isl_map *map);
1707 __isl_give isl_union_set *isl_union_map_domain(
1708 __isl_take isl_union_map *umap);
1709 __isl_give isl_union_set *isl_union_map_range(
1710 __isl_take isl_union_map *umap);
1712 __isl_give isl_basic_map *isl_basic_map_domain_map(
1713 __isl_take isl_basic_map *bmap);
1714 __isl_give isl_basic_map *isl_basic_map_range_map(
1715 __isl_take isl_basic_map *bmap);
1716 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1717 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1718 __isl_give isl_union_map *isl_union_map_domain_map(
1719 __isl_take isl_union_map *umap);
1720 __isl_give isl_union_map *isl_union_map_range_map(
1721 __isl_take isl_union_map *umap);
1723 The functions above construct a (basic, regular or union) relation
1724 that maps (a wrapped version of) the input relation to its domain or range.
1728 __isl_give isl_set *isl_set_eliminate(
1729 __isl_take isl_set *set, enum isl_dim_type type,
1730 unsigned first, unsigned n);
1731 __isl_give isl_basic_map *isl_basic_map_eliminate(
1732 __isl_take isl_basic_map *bmap,
1733 enum isl_dim_type type,
1734 unsigned first, unsigned n);
1736 Eliminate the coefficients for the given dimensions from the constraints,
1737 without removing the dimensions.
1741 __isl_give isl_basic_set *isl_basic_set_fix(
1742 __isl_take isl_basic_set *bset,
1743 enum isl_dim_type type, unsigned pos,
1745 __isl_give isl_basic_set *isl_basic_set_fix_si(
1746 __isl_take isl_basic_set *bset,
1747 enum isl_dim_type type, unsigned pos, int value);
1748 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1749 enum isl_dim_type type, unsigned pos,
1751 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1752 enum isl_dim_type type, unsigned pos, int value);
1753 __isl_give isl_basic_map *isl_basic_map_fix_si(
1754 __isl_take isl_basic_map *bmap,
1755 enum isl_dim_type type, unsigned pos, int value);
1756 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1757 enum isl_dim_type type, unsigned pos, int value);
1759 Intersect the set or relation with the hyperplane where the given
1760 dimension has the fixed given value.
1762 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1763 enum isl_dim_type type1, int pos1,
1764 enum isl_dim_type type2, int pos2);
1765 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1766 enum isl_dim_type type1, int pos1,
1767 enum isl_dim_type type2, int pos2);
1769 Intersect the set or relation with the hyperplane where the given
1770 dimensions are equal to each other.
1772 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1773 enum isl_dim_type type1, int pos1,
1774 enum isl_dim_type type2, int pos2);
1776 Intersect the relation with the hyperplane where the given
1777 dimensions have opposite values.
1781 __isl_give isl_map *isl_set_identity(
1782 __isl_take isl_set *set);
1783 __isl_give isl_union_map *isl_union_set_identity(
1784 __isl_take isl_union_set *uset);
1786 Construct an identity relation on the given (union) set.
1790 __isl_give isl_basic_set *isl_basic_map_deltas(
1791 __isl_take isl_basic_map *bmap);
1792 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1793 __isl_give isl_union_set *isl_union_map_deltas(
1794 __isl_take isl_union_map *umap);
1796 These functions return a (basic) set containing the differences
1797 between image elements and corresponding domain elements in the input.
1799 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1800 __isl_take isl_basic_map *bmap);
1801 __isl_give isl_map *isl_map_deltas_map(
1802 __isl_take isl_map *map);
1803 __isl_give isl_union_map *isl_union_map_deltas_map(
1804 __isl_take isl_union_map *umap);
1806 The functions above construct a (basic, regular or union) relation
1807 that maps (a wrapped version of) the input relation to its delta set.
1811 Simplify the representation of a set or relation by trying
1812 to combine pairs of basic sets or relations into a single
1813 basic set or relation.
1815 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1816 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1817 __isl_give isl_union_set *isl_union_set_coalesce(
1818 __isl_take isl_union_set *uset);
1819 __isl_give isl_union_map *isl_union_map_coalesce(
1820 __isl_take isl_union_map *umap);
1822 =item * Detecting equalities
1824 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1825 __isl_take isl_basic_set *bset);
1826 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1827 __isl_take isl_basic_map *bmap);
1828 __isl_give isl_set *isl_set_detect_equalities(
1829 __isl_take isl_set *set);
1830 __isl_give isl_map *isl_map_detect_equalities(
1831 __isl_take isl_map *map);
1832 __isl_give isl_union_set *isl_union_set_detect_equalities(
1833 __isl_take isl_union_set *uset);
1834 __isl_give isl_union_map *isl_union_map_detect_equalities(
1835 __isl_take isl_union_map *umap);
1837 Simplify the representation of a set or relation by detecting implicit
1840 =item * Removing redundant constraints
1842 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1843 __isl_take isl_basic_set *bset);
1844 __isl_give isl_set *isl_set_remove_redundancies(
1845 __isl_take isl_set *set);
1846 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1847 __isl_take isl_basic_map *bmap);
1848 __isl_give isl_map *isl_map_remove_redundancies(
1849 __isl_take isl_map *map);
1853 __isl_give isl_basic_set *isl_set_convex_hull(
1854 __isl_take isl_set *set);
1855 __isl_give isl_basic_map *isl_map_convex_hull(
1856 __isl_take isl_map *map);
1858 If the input set or relation has any existentially quantified
1859 variables, then the result of these operations is currently undefined.
1863 __isl_give isl_basic_set *isl_set_simple_hull(
1864 __isl_take isl_set *set);
1865 __isl_give isl_basic_map *isl_map_simple_hull(
1866 __isl_take isl_map *map);
1867 __isl_give isl_union_map *isl_union_map_simple_hull(
1868 __isl_take isl_union_map *umap);
1870 These functions compute a single basic set or relation
1871 that contains the whole input set or relation.
1872 In particular, the output is described by translates
1873 of the constraints describing the basic sets or relations in the input.
1877 (See \autoref{s:simple hull}.)
1883 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1884 __isl_take isl_basic_set *bset);
1885 __isl_give isl_basic_set *isl_set_affine_hull(
1886 __isl_take isl_set *set);
1887 __isl_give isl_union_set *isl_union_set_affine_hull(
1888 __isl_take isl_union_set *uset);
1889 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1890 __isl_take isl_basic_map *bmap);
1891 __isl_give isl_basic_map *isl_map_affine_hull(
1892 __isl_take isl_map *map);
1893 __isl_give isl_union_map *isl_union_map_affine_hull(
1894 __isl_take isl_union_map *umap);
1896 In case of union sets and relations, the affine hull is computed
1899 =item * Polyhedral hull
1901 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1902 __isl_take isl_set *set);
1903 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1904 __isl_take isl_map *map);
1905 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1906 __isl_take isl_union_set *uset);
1907 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1908 __isl_take isl_union_map *umap);
1910 These functions compute a single basic set or relation
1911 not involving any existentially quantified variables
1912 that contains the whole input set or relation.
1913 In case of union sets and relations, the polyhedral hull is computed
1916 =item * Optimization
1918 #include <isl/ilp.h>
1919 enum isl_lp_result isl_basic_set_max(
1920 __isl_keep isl_basic_set *bset,
1921 __isl_keep isl_aff *obj, isl_int *opt)
1922 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1923 __isl_keep isl_aff *obj, isl_int *opt);
1924 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1925 __isl_keep isl_aff *obj, isl_int *opt);
1927 Compute the minimum or maximum of the integer affine expression C<obj>
1928 over the points in C<set>, returning the result in C<opt>.
1929 The return value may be one of C<isl_lp_error>,
1930 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1932 =item * Parametric optimization
1934 __isl_give isl_pw_aff *isl_set_dim_min(
1935 __isl_take isl_set *set, int pos);
1936 __isl_give isl_pw_aff *isl_set_dim_max(
1937 __isl_take isl_set *set, int pos);
1939 Compute the minimum or maximum of the given set dimension as a function of the
1940 parameters, but independently of the other set dimensions.
1941 For lexicographic optimization, see L<"Lexicographic Optimization">.
1945 The following functions compute either the set of (rational) coefficient
1946 values of valid constraints for the given set or the set of (rational)
1947 values satisfying the constraints with coefficients from the given set.
1948 Internally, these two sets of functions perform essentially the
1949 same operations, except that the set of coefficients is assumed to
1950 be a cone, while the set of values may be any polyhedron.
1951 The current implementation is based on the Farkas lemma and
1952 Fourier-Motzkin elimination, but this may change or be made optional
1953 in future. In particular, future implementations may use different
1954 dualization algorithms or skip the elimination step.
1956 __isl_give isl_basic_set *isl_basic_set_coefficients(
1957 __isl_take isl_basic_set *bset);
1958 __isl_give isl_basic_set *isl_set_coefficients(
1959 __isl_take isl_set *set);
1960 __isl_give isl_union_set *isl_union_set_coefficients(
1961 __isl_take isl_union_set *bset);
1962 __isl_give isl_basic_set *isl_basic_set_solutions(
1963 __isl_take isl_basic_set *bset);
1964 __isl_give isl_basic_set *isl_set_solutions(
1965 __isl_take isl_set *set);
1966 __isl_give isl_union_set *isl_union_set_solutions(
1967 __isl_take isl_union_set *bset);
1971 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1973 __isl_give isl_union_map *isl_union_map_power(
1974 __isl_take isl_union_map *umap, int *exact);
1976 Compute a parametric representation for all positive powers I<k> of C<map>.
1977 The result maps I<k> to a nested relation corresponding to the
1978 I<k>th power of C<map>.
1979 The result may be an overapproximation. If the result is known to be exact,
1980 then C<*exact> is set to C<1>.
1982 =item * Transitive closure
1984 __isl_give isl_map *isl_map_transitive_closure(
1985 __isl_take isl_map *map, int *exact);
1986 __isl_give isl_union_map *isl_union_map_transitive_closure(
1987 __isl_take isl_union_map *umap, int *exact);
1989 Compute the transitive closure of C<map>.
1990 The result may be an overapproximation. If the result is known to be exact,
1991 then C<*exact> is set to C<1>.
1993 =item * Reaching path lengths
1995 __isl_give isl_map *isl_map_reaching_path_lengths(
1996 __isl_take isl_map *map, int *exact);
1998 Compute a relation that maps each element in the range of C<map>
1999 to the lengths of all paths composed of edges in C<map> that
2000 end up in the given element.
2001 The result may be an overapproximation. If the result is known to be exact,
2002 then C<*exact> is set to C<1>.
2003 To compute the I<maximal> path length, the resulting relation
2004 should be postprocessed by C<isl_map_lexmax>.
2005 In particular, if the input relation is a dependence relation
2006 (mapping sources to sinks), then the maximal path length corresponds
2007 to the free schedule.
2008 Note, however, that C<isl_map_lexmax> expects the maximum to be
2009 finite, so if the path lengths are unbounded (possibly due to
2010 the overapproximation), then you will get an error message.
2014 __isl_give isl_basic_set *isl_basic_map_wrap(
2015 __isl_take isl_basic_map *bmap);
2016 __isl_give isl_set *isl_map_wrap(
2017 __isl_take isl_map *map);
2018 __isl_give isl_union_set *isl_union_map_wrap(
2019 __isl_take isl_union_map *umap);
2020 __isl_give isl_basic_map *isl_basic_set_unwrap(
2021 __isl_take isl_basic_set *bset);
2022 __isl_give isl_map *isl_set_unwrap(
2023 __isl_take isl_set *set);
2024 __isl_give isl_union_map *isl_union_set_unwrap(
2025 __isl_take isl_union_set *uset);
2029 Remove any internal structure of domain (and range) of the given
2030 set or relation. If there is any such internal structure in the input,
2031 then the name of the space is also removed.
2033 __isl_give isl_basic_set *isl_basic_set_flatten(
2034 __isl_take isl_basic_set *bset);
2035 __isl_give isl_set *isl_set_flatten(
2036 __isl_take isl_set *set);
2037 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2038 __isl_take isl_basic_map *bmap);
2039 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2040 __isl_take isl_basic_map *bmap);
2041 __isl_give isl_map *isl_map_flatten_range(
2042 __isl_take isl_map *map);
2043 __isl_give isl_map *isl_map_flatten_domain(
2044 __isl_take isl_map *map);
2045 __isl_give isl_basic_map *isl_basic_map_flatten(
2046 __isl_take isl_basic_map *bmap);
2047 __isl_give isl_map *isl_map_flatten(
2048 __isl_take isl_map *map);
2050 __isl_give isl_map *isl_set_flatten_map(
2051 __isl_take isl_set *set);
2053 The function above constructs a relation
2054 that maps the input set to a flattened version of the set.
2058 Lift the input set to a space with extra dimensions corresponding
2059 to the existentially quantified variables in the input.
2060 In particular, the result lives in a wrapped map where the domain
2061 is the original space and the range corresponds to the original
2062 existentially quantified variables.
2064 __isl_give isl_basic_set *isl_basic_set_lift(
2065 __isl_take isl_basic_set *bset);
2066 __isl_give isl_set *isl_set_lift(
2067 __isl_take isl_set *set);
2068 __isl_give isl_union_set *isl_union_set_lift(
2069 __isl_take isl_union_set *uset);
2071 =item * Internal Product
2073 __isl_give isl_basic_map *isl_basic_map_zip(
2074 __isl_take isl_basic_map *bmap);
2075 __isl_give isl_map *isl_map_zip(
2076 __isl_take isl_map *map);
2077 __isl_give isl_union_map *isl_union_map_zip(
2078 __isl_take isl_union_map *umap);
2080 Given a relation with nested relations for domain and range,
2081 interchange the range of the domain with the domain of the range.
2083 =item * Aligning parameters
2085 __isl_give isl_set *isl_set_align_params(
2086 __isl_take isl_set *set,
2087 __isl_take isl_space *model);
2088 __isl_give isl_map *isl_map_align_params(
2089 __isl_take isl_map *map,
2090 __isl_take isl_space *model);
2092 Change the order of the parameters of the given set or relation
2093 such that the first parameters match those of C<model>.
2094 This may involve the introduction of extra parameters.
2095 All parameters need to be named.
2097 =item * Dimension manipulation
2099 __isl_give isl_set *isl_set_add_dims(
2100 __isl_take isl_set *set,
2101 enum isl_dim_type type, unsigned n);
2102 __isl_give isl_map *isl_map_add_dims(
2103 __isl_take isl_map *map,
2104 enum isl_dim_type type, unsigned n);
2105 __isl_give isl_set *isl_set_insert_dims(
2106 __isl_take isl_set *set,
2107 enum isl_dim_type type, unsigned pos, unsigned n);
2108 __isl_give isl_map *isl_map_insert_dims(
2109 __isl_take isl_map *map,
2110 enum isl_dim_type type, unsigned pos, unsigned n);
2111 __isl_give isl_basic_set *isl_basic_set_move_dims(
2112 __isl_take isl_basic_set *bset,
2113 enum isl_dim_type dst_type, unsigned dst_pos,
2114 enum isl_dim_type src_type, unsigned src_pos,
2116 __isl_give isl_basic_map *isl_basic_map_move_dims(
2117 __isl_take isl_basic_map *bmap,
2118 enum isl_dim_type dst_type, unsigned dst_pos,
2119 enum isl_dim_type src_type, unsigned src_pos,
2121 __isl_give isl_set *isl_set_move_dims(
2122 __isl_take isl_set *set,
2123 enum isl_dim_type dst_type, unsigned dst_pos,
2124 enum isl_dim_type src_type, unsigned src_pos,
2126 __isl_give isl_map *isl_map_move_dims(
2127 __isl_take isl_map *map,
2128 enum isl_dim_type dst_type, unsigned dst_pos,
2129 enum isl_dim_type src_type, unsigned src_pos,
2132 It is usually not advisable to directly change the (input or output)
2133 space of a set or a relation as this removes the name and the internal
2134 structure of the space. However, the above functions can be useful
2135 to add new parameters, assuming
2136 C<isl_set_align_params> and C<isl_map_align_params>
2141 =head2 Binary Operations
2143 The two arguments of a binary operation not only need to live
2144 in the same C<isl_ctx>, they currently also need to have
2145 the same (number of) parameters.
2147 =head3 Basic Operations
2151 =item * Intersection
2153 __isl_give isl_basic_set *isl_basic_set_intersect(
2154 __isl_take isl_basic_set *bset1,
2155 __isl_take isl_basic_set *bset2);
2156 __isl_give isl_set *isl_set_intersect_params(
2157 __isl_take isl_set *set,
2158 __isl_take isl_set *params);
2159 __isl_give isl_set *isl_set_intersect(
2160 __isl_take isl_set *set1,
2161 __isl_take isl_set *set2);
2162 __isl_give isl_union_set *isl_union_set_intersect(
2163 __isl_take isl_union_set *uset1,
2164 __isl_take isl_union_set *uset2);
2165 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2166 __isl_take isl_basic_map *bmap,
2167 __isl_take isl_basic_set *bset);
2168 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2169 __isl_take isl_basic_map *bmap,
2170 __isl_take isl_basic_set *bset);
2171 __isl_give isl_basic_map *isl_basic_map_intersect(
2172 __isl_take isl_basic_map *bmap1,
2173 __isl_take isl_basic_map *bmap2);
2174 __isl_give isl_map *isl_map_intersect_params(
2175 __isl_take isl_map *map,
2176 __isl_take isl_set *params);
2177 __isl_give isl_map *isl_map_intersect_domain(
2178 __isl_take isl_map *map,
2179 __isl_take isl_set *set);
2180 __isl_give isl_map *isl_map_intersect_range(
2181 __isl_take isl_map *map,
2182 __isl_take isl_set *set);
2183 __isl_give isl_map *isl_map_intersect(
2184 __isl_take isl_map *map1,
2185 __isl_take isl_map *map2);
2186 __isl_give isl_union_map *isl_union_map_intersect_domain(
2187 __isl_take isl_union_map *umap,
2188 __isl_take isl_union_set *uset);
2189 __isl_give isl_union_map *isl_union_map_intersect_range(
2190 __isl_take isl_union_map *umap,
2191 __isl_take isl_union_set *uset);
2192 __isl_give isl_union_map *isl_union_map_intersect(
2193 __isl_take isl_union_map *umap1,
2194 __isl_take isl_union_map *umap2);
2198 __isl_give isl_set *isl_basic_set_union(
2199 __isl_take isl_basic_set *bset1,
2200 __isl_take isl_basic_set *bset2);
2201 __isl_give isl_map *isl_basic_map_union(
2202 __isl_take isl_basic_map *bmap1,
2203 __isl_take isl_basic_map *bmap2);
2204 __isl_give isl_set *isl_set_union(
2205 __isl_take isl_set *set1,
2206 __isl_take isl_set *set2);
2207 __isl_give isl_map *isl_map_union(
2208 __isl_take isl_map *map1,
2209 __isl_take isl_map *map2);
2210 __isl_give isl_union_set *isl_union_set_union(
2211 __isl_take isl_union_set *uset1,
2212 __isl_take isl_union_set *uset2);
2213 __isl_give isl_union_map *isl_union_map_union(
2214 __isl_take isl_union_map *umap1,
2215 __isl_take isl_union_map *umap2);
2217 =item * Set difference
2219 __isl_give isl_set *isl_set_subtract(
2220 __isl_take isl_set *set1,
2221 __isl_take isl_set *set2);
2222 __isl_give isl_map *isl_map_subtract(
2223 __isl_take isl_map *map1,
2224 __isl_take isl_map *map2);
2225 __isl_give isl_union_set *isl_union_set_subtract(
2226 __isl_take isl_union_set *uset1,
2227 __isl_take isl_union_set *uset2);
2228 __isl_give isl_union_map *isl_union_map_subtract(
2229 __isl_take isl_union_map *umap1,
2230 __isl_take isl_union_map *umap2);
2234 __isl_give isl_basic_set *isl_basic_set_apply(
2235 __isl_take isl_basic_set *bset,
2236 __isl_take isl_basic_map *bmap);
2237 __isl_give isl_set *isl_set_apply(
2238 __isl_take isl_set *set,
2239 __isl_take isl_map *map);
2240 __isl_give isl_union_set *isl_union_set_apply(
2241 __isl_take isl_union_set *uset,
2242 __isl_take isl_union_map *umap);
2243 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2244 __isl_take isl_basic_map *bmap1,
2245 __isl_take isl_basic_map *bmap2);
2246 __isl_give isl_basic_map *isl_basic_map_apply_range(
2247 __isl_take isl_basic_map *bmap1,
2248 __isl_take isl_basic_map *bmap2);
2249 __isl_give isl_map *isl_map_apply_domain(
2250 __isl_take isl_map *map1,
2251 __isl_take isl_map *map2);
2252 __isl_give isl_union_map *isl_union_map_apply_domain(
2253 __isl_take isl_union_map *umap1,
2254 __isl_take isl_union_map *umap2);
2255 __isl_give isl_map *isl_map_apply_range(
2256 __isl_take isl_map *map1,
2257 __isl_take isl_map *map2);
2258 __isl_give isl_union_map *isl_union_map_apply_range(
2259 __isl_take isl_union_map *umap1,
2260 __isl_take isl_union_map *umap2);
2262 =item * Cartesian Product
2264 __isl_give isl_set *isl_set_product(
2265 __isl_take isl_set *set1,
2266 __isl_take isl_set *set2);
2267 __isl_give isl_union_set *isl_union_set_product(
2268 __isl_take isl_union_set *uset1,
2269 __isl_take isl_union_set *uset2);
2270 __isl_give isl_basic_map *isl_basic_map_domain_product(
2271 __isl_take isl_basic_map *bmap1,
2272 __isl_take isl_basic_map *bmap2);
2273 __isl_give isl_basic_map *isl_basic_map_range_product(
2274 __isl_take isl_basic_map *bmap1,
2275 __isl_take isl_basic_map *bmap2);
2276 __isl_give isl_map *isl_map_domain_product(
2277 __isl_take isl_map *map1,
2278 __isl_take isl_map *map2);
2279 __isl_give isl_map *isl_map_range_product(
2280 __isl_take isl_map *map1,
2281 __isl_take isl_map *map2);
2282 __isl_give isl_union_map *isl_union_map_range_product(
2283 __isl_take isl_union_map *umap1,
2284 __isl_take isl_union_map *umap2);
2285 __isl_give isl_map *isl_map_product(
2286 __isl_take isl_map *map1,
2287 __isl_take isl_map *map2);
2288 __isl_give isl_union_map *isl_union_map_product(
2289 __isl_take isl_union_map *umap1,
2290 __isl_take isl_union_map *umap2);
2292 The above functions compute the cross product of the given
2293 sets or relations. The domains and ranges of the results
2294 are wrapped maps between domains and ranges of the inputs.
2295 To obtain a ``flat'' product, use the following functions
2298 __isl_give isl_basic_set *isl_basic_set_flat_product(
2299 __isl_take isl_basic_set *bset1,
2300 __isl_take isl_basic_set *bset2);
2301 __isl_give isl_set *isl_set_flat_product(
2302 __isl_take isl_set *set1,
2303 __isl_take isl_set *set2);
2304 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2305 __isl_take isl_basic_map *bmap1,
2306 __isl_take isl_basic_map *bmap2);
2307 __isl_give isl_map *isl_map_flat_domain_product(
2308 __isl_take isl_map *map1,
2309 __isl_take isl_map *map2);
2310 __isl_give isl_map *isl_map_flat_range_product(
2311 __isl_take isl_map *map1,
2312 __isl_take isl_map *map2);
2313 __isl_give isl_union_map *isl_union_map_flat_range_product(
2314 __isl_take isl_union_map *umap1,
2315 __isl_take isl_union_map *umap2);
2316 __isl_give isl_basic_map *isl_basic_map_flat_product(
2317 __isl_take isl_basic_map *bmap1,
2318 __isl_take isl_basic_map *bmap2);
2319 __isl_give isl_map *isl_map_flat_product(
2320 __isl_take isl_map *map1,
2321 __isl_take isl_map *map2);
2323 =item * Simplification
2325 __isl_give isl_basic_set *isl_basic_set_gist(
2326 __isl_take isl_basic_set *bset,
2327 __isl_take isl_basic_set *context);
2328 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2329 __isl_take isl_set *context);
2330 __isl_give isl_set *isl_set_gist_params(
2331 __isl_take isl_set *set,
2332 __isl_take isl_set *context);
2333 __isl_give isl_union_set *isl_union_set_gist(
2334 __isl_take isl_union_set *uset,
2335 __isl_take isl_union_set *context);
2336 __isl_give isl_basic_map *isl_basic_map_gist(
2337 __isl_take isl_basic_map *bmap,
2338 __isl_take isl_basic_map *context);
2339 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2340 __isl_take isl_map *context);
2341 __isl_give isl_map *isl_map_gist_params(
2342 __isl_take isl_map *map,
2343 __isl_take isl_set *context);
2344 __isl_give isl_union_map *isl_union_map_gist(
2345 __isl_take isl_union_map *umap,
2346 __isl_take isl_union_map *context);
2348 The gist operation returns a set or relation that has the
2349 same intersection with the context as the input set or relation.
2350 Any implicit equality in the intersection is made explicit in the result,
2351 while all inequalities that are redundant with respect to the intersection
2353 In case of union sets and relations, the gist operation is performed
2358 =head3 Lexicographic Optimization
2360 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2361 the following functions
2362 compute a set that contains the lexicographic minimum or maximum
2363 of the elements in C<set> (or C<bset>) for those values of the parameters
2364 that satisfy C<dom>.
2365 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2366 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2368 In other words, the union of the parameter values
2369 for which the result is non-empty and of C<*empty>
2372 __isl_give isl_set *isl_basic_set_partial_lexmin(
2373 __isl_take isl_basic_set *bset,
2374 __isl_take isl_basic_set *dom,
2375 __isl_give isl_set **empty);
2376 __isl_give isl_set *isl_basic_set_partial_lexmax(
2377 __isl_take isl_basic_set *bset,
2378 __isl_take isl_basic_set *dom,
2379 __isl_give isl_set **empty);
2380 __isl_give isl_set *isl_set_partial_lexmin(
2381 __isl_take isl_set *set, __isl_take isl_set *dom,
2382 __isl_give isl_set **empty);
2383 __isl_give isl_set *isl_set_partial_lexmax(
2384 __isl_take isl_set *set, __isl_take isl_set *dom,
2385 __isl_give isl_set **empty);
2387 Given a (basic) set C<set> (or C<bset>), the following functions simply
2388 return a set containing the lexicographic minimum or maximum
2389 of the elements in C<set> (or C<bset>).
2390 In case of union sets, the optimum is computed per space.
2392 __isl_give isl_set *isl_basic_set_lexmin(
2393 __isl_take isl_basic_set *bset);
2394 __isl_give isl_set *isl_basic_set_lexmax(
2395 __isl_take isl_basic_set *bset);
2396 __isl_give isl_set *isl_set_lexmin(
2397 __isl_take isl_set *set);
2398 __isl_give isl_set *isl_set_lexmax(
2399 __isl_take isl_set *set);
2400 __isl_give isl_union_set *isl_union_set_lexmin(
2401 __isl_take isl_union_set *uset);
2402 __isl_give isl_union_set *isl_union_set_lexmax(
2403 __isl_take isl_union_set *uset);
2405 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2406 the following functions
2407 compute a relation that maps each element of C<dom>
2408 to the single lexicographic minimum or maximum
2409 of the elements that are associated to that same
2410 element in C<map> (or C<bmap>).
2411 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2412 that contains the elements in C<dom> that do not map
2413 to any elements in C<map> (or C<bmap>).
2414 In other words, the union of the domain of the result and of C<*empty>
2417 __isl_give isl_map *isl_basic_map_partial_lexmax(
2418 __isl_take isl_basic_map *bmap,
2419 __isl_take isl_basic_set *dom,
2420 __isl_give isl_set **empty);
2421 __isl_give isl_map *isl_basic_map_partial_lexmin(
2422 __isl_take isl_basic_map *bmap,
2423 __isl_take isl_basic_set *dom,
2424 __isl_give isl_set **empty);
2425 __isl_give isl_map *isl_map_partial_lexmax(
2426 __isl_take isl_map *map, __isl_take isl_set *dom,
2427 __isl_give isl_set **empty);
2428 __isl_give isl_map *isl_map_partial_lexmin(
2429 __isl_take isl_map *map, __isl_take isl_set *dom,
2430 __isl_give isl_set **empty);
2432 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2433 return a map mapping each element in the domain of
2434 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2435 of all elements associated to that element.
2436 In case of union relations, the optimum is computed per space.
2438 __isl_give isl_map *isl_basic_map_lexmin(
2439 __isl_take isl_basic_map *bmap);
2440 __isl_give isl_map *isl_basic_map_lexmax(
2441 __isl_take isl_basic_map *bmap);
2442 __isl_give isl_map *isl_map_lexmin(
2443 __isl_take isl_map *map);
2444 __isl_give isl_map *isl_map_lexmax(
2445 __isl_take isl_map *map);
2446 __isl_give isl_union_map *isl_union_map_lexmin(
2447 __isl_take isl_union_map *umap);
2448 __isl_give isl_union_map *isl_union_map_lexmax(
2449 __isl_take isl_union_map *umap);
2453 Lists are defined over several element types, including
2454 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2455 Here we take lists of C<isl_set>s as an example.
2456 Lists can be created, copied and freed using the following functions.
2458 #include <isl/list.h>
2459 __isl_give isl_set_list *isl_set_list_from_set(
2460 __isl_take isl_set *el);
2461 __isl_give isl_set_list *isl_set_list_alloc(
2462 isl_ctx *ctx, int n);
2463 __isl_give isl_set_list *isl_set_list_copy(
2464 __isl_keep isl_set_list *list);
2465 __isl_give isl_set_list *isl_set_list_add(
2466 __isl_take isl_set_list *list,
2467 __isl_take isl_set *el);
2468 __isl_give isl_set_list *isl_set_list_concat(
2469 __isl_take isl_set_list *list1,
2470 __isl_take isl_set_list *list2);
2471 void *isl_set_list_free(__isl_take isl_set_list *list);
2473 C<isl_set_list_alloc> creates an empty list with a capacity for
2474 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2477 Lists can be inspected using the following functions.
2479 #include <isl/list.h>
2480 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2481 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2482 __isl_give isl_set *isl_set_list_get_set(
2483 __isl_keep isl_set_list *list, int index);
2484 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2485 int (*fn)(__isl_take isl_set *el, void *user),
2488 Lists can be printed using
2490 #include <isl/list.h>
2491 __isl_give isl_printer *isl_printer_print_set_list(
2492 __isl_take isl_printer *p,
2493 __isl_keep isl_set_list *list);
2497 Matrices can be created, copied and freed using the following functions.
2499 #include <isl/mat.h>
2500 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2501 unsigned n_row, unsigned n_col);
2502 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2503 void isl_mat_free(__isl_take isl_mat *mat);
2505 Note that the elements of a newly created matrix may have arbitrary values.
2506 The elements can be changed and inspected using the following functions.
2508 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2509 int isl_mat_rows(__isl_keep isl_mat *mat);
2510 int isl_mat_cols(__isl_keep isl_mat *mat);
2511 int isl_mat_get_element(__isl_keep isl_mat *mat,
2512 int row, int col, isl_int *v);
2513 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2514 int row, int col, isl_int v);
2515 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2516 int row, int col, int v);
2518 C<isl_mat_get_element> will return a negative value if anything went wrong.
2519 In that case, the value of C<*v> is undefined.
2521 The following function can be used to compute the (right) inverse
2522 of a matrix, i.e., a matrix such that the product of the original
2523 and the inverse (in that order) is a multiple of the identity matrix.
2524 The input matrix is assumed to be of full row-rank.
2526 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2528 The following function can be used to compute the (right) kernel
2529 (or null space) of a matrix, i.e., a matrix such that the product of
2530 the original and the kernel (in that order) is the zero matrix.
2532 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2534 =head2 Piecewise Quasi Affine Expressions
2536 The zero quasi affine expression on a given domain can be created using
2538 __isl_give isl_aff *isl_aff_zero_on_domain(
2539 __isl_take isl_local_space *ls);
2541 Note that the space in which the resulting object lives is a map space
2542 with the given space as domain and a one-dimensional range.
2544 An empty piecewise quasi affine expression (one with no cells)
2545 or a piecewise quasi affine expression with a single cell can
2546 be created using the following functions.
2548 #include <isl/aff.h>
2549 __isl_give isl_pw_aff *isl_pw_aff_empty(
2550 __isl_take isl_space *space);
2551 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2552 __isl_take isl_set *set, __isl_take isl_aff *aff);
2553 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2554 __isl_take isl_aff *aff);
2556 Quasi affine expressions can be copied and freed using
2558 #include <isl/aff.h>
2559 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2560 void *isl_aff_free(__isl_take isl_aff *aff);
2562 __isl_give isl_pw_aff *isl_pw_aff_copy(
2563 __isl_keep isl_pw_aff *pwaff);
2564 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2566 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2567 using the following function. The constraint is required to have
2568 a non-zero coefficient for the specified dimension.
2570 #include <isl/constraint.h>
2571 __isl_give isl_aff *isl_constraint_get_bound(
2572 __isl_keep isl_constraint *constraint,
2573 enum isl_dim_type type, int pos);
2575 The entire affine expression of the constraint can also be extracted
2576 using the following function.
2578 #include <isl/constraint.h>
2579 __isl_give isl_aff *isl_constraint_get_aff(
2580 __isl_keep isl_constraint *constraint);
2582 Conversely, an equality constraint equating
2583 the affine expression to zero or an inequality constraint enforcing
2584 the affine expression to be non-negative, can be constructed using
2586 __isl_give isl_constraint *isl_equality_from_aff(
2587 __isl_take isl_aff *aff);
2588 __isl_give isl_constraint *isl_inequality_from_aff(
2589 __isl_take isl_aff *aff);
2591 The expression can be inspected using
2593 #include <isl/aff.h>
2594 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2595 int isl_aff_dim(__isl_keep isl_aff *aff,
2596 enum isl_dim_type type);
2597 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2598 __isl_keep isl_aff *aff);
2599 __isl_give isl_local_space *isl_aff_get_local_space(
2600 __isl_keep isl_aff *aff);
2601 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2602 enum isl_dim_type type, unsigned pos);
2603 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2605 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2606 enum isl_dim_type type, int pos, isl_int *v);
2607 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2609 __isl_give isl_aff *isl_aff_get_div(
2610 __isl_keep isl_aff *aff, int pos);
2612 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2613 int (*fn)(__isl_take isl_set *set,
2614 __isl_take isl_aff *aff,
2615 void *user), void *user);
2617 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2618 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2620 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2621 enum isl_dim_type type, unsigned first, unsigned n);
2622 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2623 enum isl_dim_type type, unsigned first, unsigned n);
2625 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2626 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2627 enum isl_dim_type type);
2628 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2630 It can be modified using
2632 #include <isl/aff.h>
2633 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2634 __isl_take isl_pw_aff *pwaff,
2635 enum isl_dim_type type, __isl_take isl_id *id);
2636 __isl_give isl_aff *isl_aff_set_dim_name(
2637 __isl_take isl_aff *aff, enum isl_dim_type type,
2638 unsigned pos, const char *s);
2639 __isl_give isl_aff *isl_aff_set_dim_id(
2640 __isl_take isl_aff *aff, enum isl_dim_type type,
2641 unsigned pos, __isl_take isl_id *id);
2642 __isl_give isl_aff *isl_aff_set_constant(
2643 __isl_take isl_aff *aff, isl_int v);
2644 __isl_give isl_aff *isl_aff_set_constant_si(
2645 __isl_take isl_aff *aff, int v);
2646 __isl_give isl_aff *isl_aff_set_coefficient(
2647 __isl_take isl_aff *aff,
2648 enum isl_dim_type type, int pos, isl_int v);
2649 __isl_give isl_aff *isl_aff_set_coefficient_si(
2650 __isl_take isl_aff *aff,
2651 enum isl_dim_type type, int pos, int v);
2652 __isl_give isl_aff *isl_aff_set_denominator(
2653 __isl_take isl_aff *aff, isl_int v);
2655 __isl_give isl_aff *isl_aff_add_constant(
2656 __isl_take isl_aff *aff, isl_int v);
2657 __isl_give isl_aff *isl_aff_add_constant_si(
2658 __isl_take isl_aff *aff, int v);
2659 __isl_give isl_aff *isl_aff_add_coefficient(
2660 __isl_take isl_aff *aff,
2661 enum isl_dim_type type, int pos, isl_int v);
2662 __isl_give isl_aff *isl_aff_add_coefficient_si(
2663 __isl_take isl_aff *aff,
2664 enum isl_dim_type type, int pos, int v);
2666 __isl_give isl_aff *isl_aff_insert_dims(
2667 __isl_take isl_aff *aff,
2668 enum isl_dim_type type, unsigned first, unsigned n);
2669 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2670 __isl_take isl_pw_aff *pwaff,
2671 enum isl_dim_type type, unsigned first, unsigned n);
2672 __isl_give isl_aff *isl_aff_add_dims(
2673 __isl_take isl_aff *aff,
2674 enum isl_dim_type type, unsigned n);
2675 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2676 __isl_take isl_pw_aff *pwaff,
2677 enum isl_dim_type type, unsigned n);
2678 __isl_give isl_aff *isl_aff_drop_dims(
2679 __isl_take isl_aff *aff,
2680 enum isl_dim_type type, unsigned first, unsigned n);
2681 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2682 __isl_take isl_pw_aff *pwaff,
2683 enum isl_dim_type type, unsigned first, unsigned n);
2685 Note that the C<set_constant> and C<set_coefficient> functions
2686 set the I<numerator> of the constant or coefficient, while
2687 C<add_constant> and C<add_coefficient> add an integer value to
2688 the possibly rational constant or coefficient.
2690 To check whether an affine expressions is obviously zero
2691 or obviously equal to some other affine expression, use
2693 #include <isl/aff.h>
2694 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2695 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2696 __isl_keep isl_aff *aff2);
2697 int isl_pw_aff_plain_is_equal(
2698 __isl_keep isl_pw_aff *pwaff1,
2699 __isl_keep isl_pw_aff *pwaff2);
2703 #include <isl/aff.h>
2704 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2705 __isl_take isl_aff *aff2);
2706 __isl_give isl_pw_aff *isl_pw_aff_add(
2707 __isl_take isl_pw_aff *pwaff1,
2708 __isl_take isl_pw_aff *pwaff2);
2709 __isl_give isl_pw_aff *isl_pw_aff_min(
2710 __isl_take isl_pw_aff *pwaff1,
2711 __isl_take isl_pw_aff *pwaff2);
2712 __isl_give isl_pw_aff *isl_pw_aff_max(
2713 __isl_take isl_pw_aff *pwaff1,
2714 __isl_take isl_pw_aff *pwaff2);
2715 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2716 __isl_take isl_aff *aff2);
2717 __isl_give isl_pw_aff *isl_pw_aff_sub(
2718 __isl_take isl_pw_aff *pwaff1,
2719 __isl_take isl_pw_aff *pwaff2);
2720 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2721 __isl_give isl_pw_aff *isl_pw_aff_neg(
2722 __isl_take isl_pw_aff *pwaff);
2723 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2724 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2725 __isl_take isl_pw_aff *pwaff);
2726 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2727 __isl_give isl_pw_aff *isl_pw_aff_floor(
2728 __isl_take isl_pw_aff *pwaff);
2729 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2731 __isl_give isl_pw_aff *isl_pw_aff_mod(
2732 __isl_take isl_pw_aff *pwaff, isl_int mod);
2733 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2735 __isl_give isl_pw_aff *isl_pw_aff_scale(
2736 __isl_take isl_pw_aff *pwaff, isl_int f);
2737 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2739 __isl_give isl_aff *isl_aff_scale_down_ui(
2740 __isl_take isl_aff *aff, unsigned f);
2741 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2742 __isl_take isl_pw_aff *pwaff, isl_int f);
2744 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2745 __isl_take isl_pw_aff_list *list);
2746 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2747 __isl_take isl_pw_aff_list *list);
2749 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2750 __isl_take isl_pw_aff *pwqp);
2752 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2753 __isl_take isl_pw_aff *pwaff,
2754 __isl_take isl_space *model);
2756 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2757 __isl_take isl_set *context);
2758 __isl_give isl_pw_aff *isl_pw_aff_gist(
2759 __isl_take isl_pw_aff *pwaff,
2760 __isl_take isl_set *context);
2762 __isl_give isl_set *isl_pw_aff_domain(
2763 __isl_take isl_pw_aff *pwaff);
2764 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2765 __isl_take isl_pw_aff *pa,
2766 __isl_take isl_set *set);
2768 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2769 __isl_take isl_aff *aff2);
2770 __isl_give isl_pw_aff *isl_pw_aff_mul(
2771 __isl_take isl_pw_aff *pwaff1,
2772 __isl_take isl_pw_aff *pwaff2);
2774 When multiplying two affine expressions, at least one of the two needs
2777 #include <isl/aff.h>
2778 __isl_give isl_basic_set *isl_aff_le_basic_set(
2779 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2780 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2781 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2782 __isl_give isl_set *isl_pw_aff_eq_set(
2783 __isl_take isl_pw_aff *pwaff1,
2784 __isl_take isl_pw_aff *pwaff2);
2785 __isl_give isl_set *isl_pw_aff_ne_set(
2786 __isl_take isl_pw_aff *pwaff1,
2787 __isl_take isl_pw_aff *pwaff2);
2788 __isl_give isl_set *isl_pw_aff_le_set(
2789 __isl_take isl_pw_aff *pwaff1,
2790 __isl_take isl_pw_aff *pwaff2);
2791 __isl_give isl_set *isl_pw_aff_lt_set(
2792 __isl_take isl_pw_aff *pwaff1,
2793 __isl_take isl_pw_aff *pwaff2);
2794 __isl_give isl_set *isl_pw_aff_ge_set(
2795 __isl_take isl_pw_aff *pwaff1,
2796 __isl_take isl_pw_aff *pwaff2);
2797 __isl_give isl_set *isl_pw_aff_gt_set(
2798 __isl_take isl_pw_aff *pwaff1,
2799 __isl_take isl_pw_aff *pwaff2);
2801 __isl_give isl_set *isl_pw_aff_list_eq_set(
2802 __isl_take isl_pw_aff_list *list1,
2803 __isl_take isl_pw_aff_list *list2);
2804 __isl_give isl_set *isl_pw_aff_list_ne_set(
2805 __isl_take isl_pw_aff_list *list1,
2806 __isl_take isl_pw_aff_list *list2);
2807 __isl_give isl_set *isl_pw_aff_list_le_set(
2808 __isl_take isl_pw_aff_list *list1,
2809 __isl_take isl_pw_aff_list *list2);
2810 __isl_give isl_set *isl_pw_aff_list_lt_set(
2811 __isl_take isl_pw_aff_list *list1,
2812 __isl_take isl_pw_aff_list *list2);
2813 __isl_give isl_set *isl_pw_aff_list_ge_set(
2814 __isl_take isl_pw_aff_list *list1,
2815 __isl_take isl_pw_aff_list *list2);
2816 __isl_give isl_set *isl_pw_aff_list_gt_set(
2817 __isl_take isl_pw_aff_list *list1,
2818 __isl_take isl_pw_aff_list *list2);
2820 The function C<isl_aff_ge_basic_set> returns a basic set
2821 containing those elements in the shared space
2822 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2823 The function C<isl_aff_ge_set> returns a set
2824 containing those elements in the shared domain
2825 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2826 The functions operating on C<isl_pw_aff_list> apply the corresponding
2827 C<isl_pw_aff> function to each pair of elements in the two lists.
2829 #include <isl/aff.h>
2830 __isl_give isl_set *isl_pw_aff_nonneg_set(
2831 __isl_take isl_pw_aff *pwaff);
2832 __isl_give isl_set *isl_pw_aff_zero_set(
2833 __isl_take isl_pw_aff *pwaff);
2834 __isl_give isl_set *isl_pw_aff_non_zero_set(
2835 __isl_take isl_pw_aff *pwaff);
2837 The function C<isl_pw_aff_nonneg_set> returns a set
2838 containing those elements in the domain
2839 of C<pwaff> where C<pwaff> is non-negative.
2841 #include <isl/aff.h>
2842 __isl_give isl_pw_aff *isl_pw_aff_cond(
2843 __isl_take isl_set *cond,
2844 __isl_take isl_pw_aff *pwaff_true,
2845 __isl_take isl_pw_aff *pwaff_false);
2847 The function C<isl_pw_aff_cond> performs a conditional operator
2848 and returns an expression that is equal to C<pwaff_true>
2849 for elements in C<cond> and equal to C<pwaff_false> for elements
2852 #include <isl/aff.h>
2853 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2854 __isl_take isl_pw_aff *pwaff1,
2855 __isl_take isl_pw_aff *pwaff2);
2856 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2857 __isl_take isl_pw_aff *pwaff1,
2858 __isl_take isl_pw_aff *pwaff2);
2860 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2861 expression with a domain that is the union of those of C<pwaff1> and
2862 C<pwaff2> and such that on each cell, the quasi-affine expression is
2863 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2864 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2865 associated expression is the defined one.
2867 An expression can be printed using
2869 #include <isl/aff.h>
2870 __isl_give isl_printer *isl_printer_print_aff(
2871 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2873 __isl_give isl_printer *isl_printer_print_pw_aff(
2874 __isl_take isl_printer *p,
2875 __isl_keep isl_pw_aff *pwaff);
2879 Points are elements of a set. They can be used to construct
2880 simple sets (boxes) or they can be used to represent the
2881 individual elements of a set.
2882 The zero point (the origin) can be created using
2884 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2886 The coordinates of a point can be inspected, set and changed
2889 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2890 enum isl_dim_type type, int pos, isl_int *v);
2891 __isl_give isl_point *isl_point_set_coordinate(
2892 __isl_take isl_point *pnt,
2893 enum isl_dim_type type, int pos, isl_int v);
2895 __isl_give isl_point *isl_point_add_ui(
2896 __isl_take isl_point *pnt,
2897 enum isl_dim_type type, int pos, unsigned val);
2898 __isl_give isl_point *isl_point_sub_ui(
2899 __isl_take isl_point *pnt,
2900 enum isl_dim_type type, int pos, unsigned val);
2902 Other properties can be obtained using
2904 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2906 Points can be copied or freed using
2908 __isl_give isl_point *isl_point_copy(
2909 __isl_keep isl_point *pnt);
2910 void isl_point_free(__isl_take isl_point *pnt);
2912 A singleton set can be created from a point using
2914 __isl_give isl_basic_set *isl_basic_set_from_point(
2915 __isl_take isl_point *pnt);
2916 __isl_give isl_set *isl_set_from_point(
2917 __isl_take isl_point *pnt);
2919 and a box can be created from two opposite extremal points using
2921 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2922 __isl_take isl_point *pnt1,
2923 __isl_take isl_point *pnt2);
2924 __isl_give isl_set *isl_set_box_from_points(
2925 __isl_take isl_point *pnt1,
2926 __isl_take isl_point *pnt2);
2928 All elements of a B<bounded> (union) set can be enumerated using
2929 the following functions.
2931 int isl_set_foreach_point(__isl_keep isl_set *set,
2932 int (*fn)(__isl_take isl_point *pnt, void *user),
2934 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2935 int (*fn)(__isl_take isl_point *pnt, void *user),
2938 The function C<fn> is called for each integer point in
2939 C<set> with as second argument the last argument of
2940 the C<isl_set_foreach_point> call. The function C<fn>
2941 should return C<0> on success and C<-1> on failure.
2942 In the latter case, C<isl_set_foreach_point> will stop
2943 enumerating and return C<-1> as well.
2944 If the enumeration is performed successfully and to completion,
2945 then C<isl_set_foreach_point> returns C<0>.
2947 To obtain a single point of a (basic) set, use
2949 __isl_give isl_point *isl_basic_set_sample_point(
2950 __isl_take isl_basic_set *bset);
2951 __isl_give isl_point *isl_set_sample_point(
2952 __isl_take isl_set *set);
2954 If C<set> does not contain any (integer) points, then the
2955 resulting point will be ``void'', a property that can be
2958 int isl_point_is_void(__isl_keep isl_point *pnt);
2960 =head2 Piecewise Quasipolynomials
2962 A piecewise quasipolynomial is a particular kind of function that maps
2963 a parametric point to a rational value.
2964 More specifically, a quasipolynomial is a polynomial expression in greatest
2965 integer parts of affine expressions of parameters and variables.
2966 A piecewise quasipolynomial is a subdivision of a given parametric
2967 domain into disjoint cells with a quasipolynomial associated to
2968 each cell. The value of the piecewise quasipolynomial at a given
2969 point is the value of the quasipolynomial associated to the cell
2970 that contains the point. Outside of the union of cells,
2971 the value is assumed to be zero.
2972 For example, the piecewise quasipolynomial
2974 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2976 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2977 A given piecewise quasipolynomial has a fixed domain dimension.
2978 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2979 defined over different domains.
2980 Piecewise quasipolynomials are mainly used by the C<barvinok>
2981 library for representing the number of elements in a parametric set or map.
2982 For example, the piecewise quasipolynomial above represents
2983 the number of points in the map
2985 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2987 =head3 Printing (Piecewise) Quasipolynomials
2989 Quasipolynomials and piecewise quasipolynomials can be printed
2990 using the following functions.
2992 __isl_give isl_printer *isl_printer_print_qpolynomial(
2993 __isl_take isl_printer *p,
2994 __isl_keep isl_qpolynomial *qp);
2996 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2997 __isl_take isl_printer *p,
2998 __isl_keep isl_pw_qpolynomial *pwqp);
3000 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3001 __isl_take isl_printer *p,
3002 __isl_keep isl_union_pw_qpolynomial *upwqp);
3004 The output format of the printer
3005 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3006 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3008 In case of printing in C<ISL_FORMAT_C>, the user may want
3009 to set the names of all dimensions
3011 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3012 __isl_take isl_qpolynomial *qp,
3013 enum isl_dim_type type, unsigned pos,
3015 __isl_give isl_pw_qpolynomial *
3016 isl_pw_qpolynomial_set_dim_name(
3017 __isl_take isl_pw_qpolynomial *pwqp,
3018 enum isl_dim_type type, unsigned pos,
3021 =head3 Creating New (Piecewise) Quasipolynomials
3023 Some simple quasipolynomials can be created using the following functions.
3024 More complicated quasipolynomials can be created by applying
3025 operations such as addition and multiplication
3026 on the resulting quasipolynomials
3028 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3029 __isl_take isl_space *domain);
3030 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3031 __isl_take isl_space *domain);
3032 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3033 __isl_take isl_space *domain);
3034 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3035 __isl_take isl_space *domain);
3036 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3037 __isl_take isl_space *domain);
3038 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3039 __isl_take isl_space *domain,
3040 const isl_int n, const isl_int d);
3041 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3042 __isl_take isl_space *domain,
3043 enum isl_dim_type type, unsigned pos);
3044 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3045 __isl_take isl_aff *aff);
3047 Note that the space in which a quasipolynomial lives is a map space
3048 with a one-dimensional range. The C<domain> argument in some of
3049 the functions above corresponds to the domain of this map space.
3051 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3052 with a single cell can be created using the following functions.
3053 Multiple of these single cell piecewise quasipolynomials can
3054 be combined to create more complicated piecewise quasipolynomials.
3056 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3057 __isl_take isl_space *space);
3058 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3059 __isl_take isl_set *set,
3060 __isl_take isl_qpolynomial *qp);
3061 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3062 __isl_take isl_qpolynomial *qp);
3063 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3064 __isl_take isl_pw_aff *pwaff);
3066 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3067 __isl_take isl_space *space);
3068 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3069 __isl_take isl_pw_qpolynomial *pwqp);
3070 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3071 __isl_take isl_union_pw_qpolynomial *upwqp,
3072 __isl_take isl_pw_qpolynomial *pwqp);
3074 Quasipolynomials can be copied and freed again using the following
3077 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3078 __isl_keep isl_qpolynomial *qp);
3079 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3081 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3082 __isl_keep isl_pw_qpolynomial *pwqp);
3083 void *isl_pw_qpolynomial_free(
3084 __isl_take isl_pw_qpolynomial *pwqp);
3086 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3087 __isl_keep isl_union_pw_qpolynomial *upwqp);
3088 void isl_union_pw_qpolynomial_free(
3089 __isl_take isl_union_pw_qpolynomial *upwqp);
3091 =head3 Inspecting (Piecewise) Quasipolynomials
3093 To iterate over all piecewise quasipolynomials in a union
3094 piecewise quasipolynomial, use the following function
3096 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3097 __isl_keep isl_union_pw_qpolynomial *upwqp,
3098 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3101 To extract the piecewise quasipolynomial in a given space from a union, use
3103 __isl_give isl_pw_qpolynomial *
3104 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3105 __isl_keep isl_union_pw_qpolynomial *upwqp,
3106 __isl_take isl_space *space);
3108 To iterate over the cells in a piecewise quasipolynomial,
3109 use either of the following two functions
3111 int isl_pw_qpolynomial_foreach_piece(
3112 __isl_keep isl_pw_qpolynomial *pwqp,
3113 int (*fn)(__isl_take isl_set *set,
3114 __isl_take isl_qpolynomial *qp,
3115 void *user), void *user);
3116 int isl_pw_qpolynomial_foreach_lifted_piece(
3117 __isl_keep isl_pw_qpolynomial *pwqp,
3118 int (*fn)(__isl_take isl_set *set,
3119 __isl_take isl_qpolynomial *qp,
3120 void *user), void *user);
3122 As usual, the function C<fn> should return C<0> on success
3123 and C<-1> on failure. The difference between
3124 C<isl_pw_qpolynomial_foreach_piece> and
3125 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3126 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3127 compute unique representations for all existentially quantified
3128 variables and then turn these existentially quantified variables
3129 into extra set variables, adapting the associated quasipolynomial
3130 accordingly. This means that the C<set> passed to C<fn>
3131 will not have any existentially quantified variables, but that
3132 the dimensions of the sets may be different for different
3133 invocations of C<fn>.
3135 To iterate over all terms in a quasipolynomial,
3138 int isl_qpolynomial_foreach_term(
3139 __isl_keep isl_qpolynomial *qp,
3140 int (*fn)(__isl_take isl_term *term,
3141 void *user), void *user);
3143 The terms themselves can be inspected and freed using
3146 unsigned isl_term_dim(__isl_keep isl_term *term,
3147 enum isl_dim_type type);
3148 void isl_term_get_num(__isl_keep isl_term *term,
3150 void isl_term_get_den(__isl_keep isl_term *term,
3152 int isl_term_get_exp(__isl_keep isl_term *term,
3153 enum isl_dim_type type, unsigned pos);
3154 __isl_give isl_aff *isl_term_get_div(
3155 __isl_keep isl_term *term, unsigned pos);
3156 void isl_term_free(__isl_take isl_term *term);
3158 Each term is a product of parameters, set variables and
3159 integer divisions. The function C<isl_term_get_exp>
3160 returns the exponent of a given dimensions in the given term.
3161 The C<isl_int>s in the arguments of C<isl_term_get_num>
3162 and C<isl_term_get_den> need to have been initialized
3163 using C<isl_int_init> before calling these functions.
3165 =head3 Properties of (Piecewise) Quasipolynomials
3167 To check whether a quasipolynomial is actually a constant,
3168 use the following function.
3170 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3171 isl_int *n, isl_int *d);
3173 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3174 then the numerator and denominator of the constant
3175 are returned in C<*n> and C<*d>, respectively.
3177 To check whether two union piecewise quasipolynomials are
3178 obviously equal, use
3180 int isl_union_pw_qpolynomial_plain_is_equal(
3181 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3182 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3184 =head3 Operations on (Piecewise) Quasipolynomials
3186 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3187 __isl_take isl_qpolynomial *qp, isl_int v);
3188 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3189 __isl_take isl_qpolynomial *qp);
3190 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3191 __isl_take isl_qpolynomial *qp1,
3192 __isl_take isl_qpolynomial *qp2);
3193 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3194 __isl_take isl_qpolynomial *qp1,
3195 __isl_take isl_qpolynomial *qp2);
3196 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3197 __isl_take isl_qpolynomial *qp1,
3198 __isl_take isl_qpolynomial *qp2);
3199 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3200 __isl_take isl_qpolynomial *qp, unsigned exponent);
3202 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3203 __isl_take isl_pw_qpolynomial *pwqp1,
3204 __isl_take isl_pw_qpolynomial *pwqp2);
3205 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3206 __isl_take isl_pw_qpolynomial *pwqp1,
3207 __isl_take isl_pw_qpolynomial *pwqp2);
3208 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3209 __isl_take isl_pw_qpolynomial *pwqp1,
3210 __isl_take isl_pw_qpolynomial *pwqp2);
3211 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3212 __isl_take isl_pw_qpolynomial *pwqp);
3213 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3214 __isl_take isl_pw_qpolynomial *pwqp1,
3215 __isl_take isl_pw_qpolynomial *pwqp2);
3216 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3217 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3219 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3220 __isl_take isl_union_pw_qpolynomial *upwqp1,
3221 __isl_take isl_union_pw_qpolynomial *upwqp2);
3222 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3223 __isl_take isl_union_pw_qpolynomial *upwqp1,
3224 __isl_take isl_union_pw_qpolynomial *upwqp2);
3225 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3226 __isl_take isl_union_pw_qpolynomial *upwqp1,
3227 __isl_take isl_union_pw_qpolynomial *upwqp2);
3229 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3230 __isl_take isl_pw_qpolynomial *pwqp,
3231 __isl_take isl_point *pnt);
3233 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3234 __isl_take isl_union_pw_qpolynomial *upwqp,
3235 __isl_take isl_point *pnt);
3237 __isl_give isl_set *isl_pw_qpolynomial_domain(
3238 __isl_take isl_pw_qpolynomial *pwqp);
3239 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3240 __isl_take isl_pw_qpolynomial *pwpq,
3241 __isl_take isl_set *set);
3243 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3244 __isl_take isl_union_pw_qpolynomial *upwqp);
3245 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3246 __isl_take isl_union_pw_qpolynomial *upwpq,
3247 __isl_take isl_union_set *uset);
3249 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3250 __isl_take isl_qpolynomial *qp,
3251 __isl_take isl_space *model);
3253 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3254 __isl_take isl_qpolynomial *qp);
3255 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3256 __isl_take isl_pw_qpolynomial *pwqp);
3258 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3259 __isl_take isl_union_pw_qpolynomial *upwqp);
3261 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3262 __isl_take isl_qpolynomial *qp,
3263 __isl_take isl_set *context);
3265 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3266 __isl_take isl_pw_qpolynomial *pwqp,
3267 __isl_take isl_set *context);
3269 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3270 __isl_take isl_union_pw_qpolynomial *upwqp,
3271 __isl_take isl_union_set *context);
3273 The gist operation applies the gist operation to each of
3274 the cells in the domain of the input piecewise quasipolynomial.
3275 The context is also exploited
3276 to simplify the quasipolynomials associated to each cell.
3278 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3279 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3280 __isl_give isl_union_pw_qpolynomial *
3281 isl_union_pw_qpolynomial_to_polynomial(
3282 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3284 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3285 the polynomial will be an overapproximation. If C<sign> is negative,
3286 it will be an underapproximation. If C<sign> is zero, the approximation
3287 will lie somewhere in between.
3289 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3291 A piecewise quasipolynomial reduction is a piecewise
3292 reduction (or fold) of quasipolynomials.
3293 In particular, the reduction can be maximum or a minimum.
3294 The objects are mainly used to represent the result of
3295 an upper or lower bound on a quasipolynomial over its domain,
3296 i.e., as the result of the following function.
3298 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3299 __isl_take isl_pw_qpolynomial *pwqp,
3300 enum isl_fold type, int *tight);
3302 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3303 __isl_take isl_union_pw_qpolynomial *upwqp,
3304 enum isl_fold type, int *tight);
3306 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3307 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3308 is the returned bound is known be tight, i.e., for each value
3309 of the parameters there is at least
3310 one element in the domain that reaches the bound.
3311 If the domain of C<pwqp> is not wrapping, then the bound is computed
3312 over all elements in that domain and the result has a purely parametric
3313 domain. If the domain of C<pwqp> is wrapping, then the bound is
3314 computed over the range of the wrapped relation. The domain of the
3315 wrapped relation becomes the domain of the result.
3317 A (piecewise) quasipolynomial reduction can be copied or freed using the
3318 following functions.
3320 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3321 __isl_keep isl_qpolynomial_fold *fold);
3322 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3323 __isl_keep isl_pw_qpolynomial_fold *pwf);
3324 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3325 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3326 void isl_qpolynomial_fold_free(
3327 __isl_take isl_qpolynomial_fold *fold);
3328 void *isl_pw_qpolynomial_fold_free(
3329 __isl_take isl_pw_qpolynomial_fold *pwf);
3330 void isl_union_pw_qpolynomial_fold_free(
3331 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3333 =head3 Printing Piecewise Quasipolynomial Reductions
3335 Piecewise quasipolynomial reductions can be printed
3336 using the following function.
3338 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3339 __isl_take isl_printer *p,
3340 __isl_keep isl_pw_qpolynomial_fold *pwf);
3341 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3342 __isl_take isl_printer *p,
3343 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3345 For C<isl_printer_print_pw_qpolynomial_fold>,
3346 output format of the printer
3347 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3348 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3349 output format of the printer
3350 needs to be set to C<ISL_FORMAT_ISL>.
3351 In case of printing in C<ISL_FORMAT_C>, the user may want
3352 to set the names of all dimensions
3354 __isl_give isl_pw_qpolynomial_fold *
3355 isl_pw_qpolynomial_fold_set_dim_name(
3356 __isl_take isl_pw_qpolynomial_fold *pwf,
3357 enum isl_dim_type type, unsigned pos,
3360 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3362 To iterate over all piecewise quasipolynomial reductions in a union
3363 piecewise quasipolynomial reduction, use the following function
3365 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3366 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3367 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3368 void *user), void *user);
3370 To iterate over the cells in a piecewise quasipolynomial reduction,
3371 use either of the following two functions
3373 int isl_pw_qpolynomial_fold_foreach_piece(
3374 __isl_keep isl_pw_qpolynomial_fold *pwf,
3375 int (*fn)(__isl_take isl_set *set,
3376 __isl_take isl_qpolynomial_fold *fold,
3377 void *user), void *user);
3378 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3379 __isl_keep isl_pw_qpolynomial_fold *pwf,
3380 int (*fn)(__isl_take isl_set *set,
3381 __isl_take isl_qpolynomial_fold *fold,
3382 void *user), void *user);
3384 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3385 of the difference between these two functions.
3387 To iterate over all quasipolynomials in a reduction, use
3389 int isl_qpolynomial_fold_foreach_qpolynomial(
3390 __isl_keep isl_qpolynomial_fold *fold,
3391 int (*fn)(__isl_take isl_qpolynomial *qp,
3392 void *user), void *user);
3394 =head3 Properties of Piecewise Quasipolynomial Reductions
3396 To check whether two union piecewise quasipolynomial reductions are
3397 obviously equal, use
3399 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3400 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3401 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3403 =head3 Operations on Piecewise Quasipolynomial Reductions
3405 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3406 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3408 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3409 __isl_take isl_pw_qpolynomial_fold *pwf1,
3410 __isl_take isl_pw_qpolynomial_fold *pwf2);
3412 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3413 __isl_take isl_pw_qpolynomial_fold *pwf1,
3414 __isl_take isl_pw_qpolynomial_fold *pwf2);
3416 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3417 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3418 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3420 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3421 __isl_take isl_pw_qpolynomial_fold *pwf,
3422 __isl_take isl_point *pnt);
3424 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3425 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3426 __isl_take isl_point *pnt);
3428 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3429 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3430 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3431 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3432 __isl_take isl_union_set *uset);
3434 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3435 __isl_take isl_pw_qpolynomial_fold *pwf);
3437 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3438 __isl_take isl_pw_qpolynomial_fold *pwf);
3440 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3441 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3443 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3444 __isl_take isl_pw_qpolynomial_fold *pwf,
3445 __isl_take isl_set *context);
3447 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3448 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3449 __isl_take isl_union_set *context);
3451 The gist operation applies the gist operation to each of
3452 the cells in the domain of the input piecewise quasipolynomial reduction.
3453 In future, the operation will also exploit the context
3454 to simplify the quasipolynomial reductions associated to each cell.
3456 __isl_give isl_pw_qpolynomial_fold *
3457 isl_set_apply_pw_qpolynomial_fold(
3458 __isl_take isl_set *set,
3459 __isl_take isl_pw_qpolynomial_fold *pwf,
3461 __isl_give isl_pw_qpolynomial_fold *
3462 isl_map_apply_pw_qpolynomial_fold(
3463 __isl_take isl_map *map,
3464 __isl_take isl_pw_qpolynomial_fold *pwf,
3466 __isl_give isl_union_pw_qpolynomial_fold *
3467 isl_union_set_apply_union_pw_qpolynomial_fold(
3468 __isl_take isl_union_set *uset,
3469 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3471 __isl_give isl_union_pw_qpolynomial_fold *
3472 isl_union_map_apply_union_pw_qpolynomial_fold(
3473 __isl_take isl_union_map *umap,
3474 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3477 The functions taking a map
3478 compose the given map with the given piecewise quasipolynomial reduction.
3479 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3480 over all elements in the intersection of the range of the map
3481 and the domain of the piecewise quasipolynomial reduction
3482 as a function of an element in the domain of the map.
3483 The functions taking a set compute a bound over all elements in the
3484 intersection of the set and the domain of the
3485 piecewise quasipolynomial reduction.
3487 =head2 Dependence Analysis
3489 C<isl> contains specialized functionality for performing
3490 array dataflow analysis. That is, given a I<sink> access relation
3491 and a collection of possible I<source> access relations,
3492 C<isl> can compute relations that describe
3493 for each iteration of the sink access, which iteration
3494 of which of the source access relations was the last
3495 to access the same data element before the given iteration
3497 To compute standard flow dependences, the sink should be
3498 a read, while the sources should be writes.
3499 If any of the source accesses are marked as being I<may>
3500 accesses, then there will be a dependence to the last
3501 I<must> access B<and> to any I<may> access that follows
3502 this last I<must> access.
3503 In particular, if I<all> sources are I<may> accesses,
3504 then memory based dependence analysis is performed.
3505 If, on the other hand, all sources are I<must> accesses,
3506 then value based dependence analysis is performed.
3508 #include <isl/flow.h>
3510 typedef int (*isl_access_level_before)(void *first, void *second);
3512 __isl_give isl_access_info *isl_access_info_alloc(
3513 __isl_take isl_map *sink,
3514 void *sink_user, isl_access_level_before fn,
3516 __isl_give isl_access_info *isl_access_info_add_source(
3517 __isl_take isl_access_info *acc,
3518 __isl_take isl_map *source, int must,
3520 void isl_access_info_free(__isl_take isl_access_info *acc);
3522 __isl_give isl_flow *isl_access_info_compute_flow(
3523 __isl_take isl_access_info *acc);
3525 int isl_flow_foreach(__isl_keep isl_flow *deps,
3526 int (*fn)(__isl_take isl_map *dep, int must,
3527 void *dep_user, void *user),
3529 __isl_give isl_map *isl_flow_get_no_source(
3530 __isl_keep isl_flow *deps, int must);
3531 void isl_flow_free(__isl_take isl_flow *deps);
3533 The function C<isl_access_info_compute_flow> performs the actual
3534 dependence analysis. The other functions are used to construct
3535 the input for this function or to read off the output.
3537 The input is collected in an C<isl_access_info>, which can
3538 be created through a call to C<isl_access_info_alloc>.
3539 The arguments to this functions are the sink access relation
3540 C<sink>, a token C<sink_user> used to identify the sink
3541 access to the user, a callback function for specifying the
3542 relative order of source and sink accesses, and the number
3543 of source access relations that will be added.
3544 The callback function has type C<int (*)(void *first, void *second)>.
3545 The function is called with two user supplied tokens identifying
3546 either a source or the sink and it should return the shared nesting
3547 level and the relative order of the two accesses.
3548 In particular, let I<n> be the number of loops shared by
3549 the two accesses. If C<first> precedes C<second> textually,
3550 then the function should return I<2 * n + 1>; otherwise,
3551 it should return I<2 * n>.
3552 The sources can be added to the C<isl_access_info> by performing
3553 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3554 C<must> indicates whether the source is a I<must> access
3555 or a I<may> access. Note that a multi-valued access relation
3556 should only be marked I<must> if every iteration in the domain
3557 of the relation accesses I<all> elements in its image.
3558 The C<source_user> token is again used to identify
3559 the source access. The range of the source access relation
3560 C<source> should have the same dimension as the range
3561 of the sink access relation.
3562 The C<isl_access_info_free> function should usually not be
3563 called explicitly, because it is called implicitly by
3564 C<isl_access_info_compute_flow>.
3566 The result of the dependence analysis is collected in an
3567 C<isl_flow>. There may be elements of
3568 the sink access for which no preceding source access could be
3569 found or for which all preceding sources are I<may> accesses.
3570 The relations containing these elements can be obtained through
3571 calls to C<isl_flow_get_no_source>, the first with C<must> set
3572 and the second with C<must> unset.
3573 In the case of standard flow dependence analysis,
3574 with the sink a read and the sources I<must> writes,
3575 the first relation corresponds to the reads from uninitialized
3576 array elements and the second relation is empty.
3577 The actual flow dependences can be extracted using
3578 C<isl_flow_foreach>. This function will call the user-specified
3579 callback function C<fn> for each B<non-empty> dependence between
3580 a source and the sink. The callback function is called
3581 with four arguments, the actual flow dependence relation
3582 mapping source iterations to sink iterations, a boolean that
3583 indicates whether it is a I<must> or I<may> dependence, a token
3584 identifying the source and an additional C<void *> with value
3585 equal to the third argument of the C<isl_flow_foreach> call.
3586 A dependence is marked I<must> if it originates from a I<must>
3587 source and if it is not followed by any I<may> sources.
3589 After finishing with an C<isl_flow>, the user should call
3590 C<isl_flow_free> to free all associated memory.
3592 A higher-level interface to dependence analysis is provided
3593 by the following function.
3595 #include <isl/flow.h>
3597 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3598 __isl_take isl_union_map *must_source,
3599 __isl_take isl_union_map *may_source,
3600 __isl_take isl_union_map *schedule,
3601 __isl_give isl_union_map **must_dep,
3602 __isl_give isl_union_map **may_dep,
3603 __isl_give isl_union_map **must_no_source,
3604 __isl_give isl_union_map **may_no_source);
3606 The arrays are identified by the tuple names of the ranges
3607 of the accesses. The iteration domains by the tuple names
3608 of the domains of the accesses and of the schedule.
3609 The relative order of the iteration domains is given by the
3610 schedule. The relations returned through C<must_no_source>
3611 and C<may_no_source> are subsets of C<sink>.
3612 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3613 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3614 any of the other arguments is treated as an error.
3618 B<The functionality described in this section is fairly new
3619 and may be subject to change.>
3621 The following function can be used to compute a schedule
3622 for a union of domains. The generated schedule respects
3623 all C<validity> dependences. That is, all dependence distances
3624 over these dependences in the scheduled space are lexicographically
3625 positive. The generated schedule schedule also tries to minimize
3626 the dependence distances over C<proximity> dependences.
3627 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3628 for groups of domains where the dependence distances have only
3629 non-negative values.
3630 The algorithm used to construct the schedule is similar to that
3633 #include <isl/schedule.h>
3634 __isl_give isl_schedule *isl_union_set_compute_schedule(
3635 __isl_take isl_union_set *domain,
3636 __isl_take isl_union_map *validity,
3637 __isl_take isl_union_map *proximity);
3638 void *isl_schedule_free(__isl_take isl_schedule *sched);
3640 A mapping from the domains to the scheduled space can be obtained
3641 from an C<isl_schedule> using the following function.
3643 __isl_give isl_union_map *isl_schedule_get_map(
3644 __isl_keep isl_schedule *sched);
3646 A representation of the schedule can be printed using
3648 __isl_give isl_printer *isl_printer_print_schedule(
3649 __isl_take isl_printer *p,
3650 __isl_keep isl_schedule *schedule);
3652 A representation of the schedule as a forest of bands can be obtained
3653 using the following function.
3655 __isl_give isl_band_list *isl_schedule_get_band_forest(
3656 __isl_keep isl_schedule *schedule);
3658 The list can be manipulated as explained in L<"Lists">.
3659 The bands inside the list can be copied and freed using the following
3662 #include <isl/band.h>
3663 __isl_give isl_band *isl_band_copy(
3664 __isl_keep isl_band *band);
3665 void *isl_band_free(__isl_take isl_band *band);
3667 Each band contains zero or more scheduling dimensions.
3668 These are referred to as the members of the band.
3669 The section of the schedule that corresponds to the band is
3670 referred to as the partial schedule of the band.
3671 For those nodes that participate in a band, the outer scheduling
3672 dimensions form the prefix schedule, while the inner scheduling
3673 dimensions form the suffix schedule.
3674 That is, if we take a cut of the band forest, then the union of
3675 the concatenations of the prefix, partial and suffix schedules of
3676 each band in the cut is equal to the entire schedule (modulo
3677 some possible padding at the end with zero scheduling dimensions).
3678 The properties of a band can be inspected using the following functions.
3680 #include <isl/band.h>
3681 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3683 int isl_band_has_children(__isl_keep isl_band *band);
3684 __isl_give isl_band_list *isl_band_get_children(
3685 __isl_keep isl_band *band);
3687 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3688 __isl_keep isl_band *band);
3689 __isl_give isl_union_map *isl_band_get_partial_schedule(
3690 __isl_keep isl_band *band);
3691 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3692 __isl_keep isl_band *band);
3694 int isl_band_n_member(__isl_keep isl_band *band);
3695 int isl_band_member_is_zero_distance(
3696 __isl_keep isl_band *band, int pos);
3698 Note that a scheduling dimension is considered to be ``zero
3699 distance'' if it does not carry any proximity dependences
3701 That is, if the dependence distances of the proximity
3702 dependences are all zero in that direction (for fixed
3703 iterations of outer bands).
3705 A representation of the band can be printed using
3707 #include <isl/band.h>
3708 __isl_give isl_printer *isl_printer_print_band(
3709 __isl_take isl_printer *p,
3710 __isl_keep isl_band *band);
3712 =head2 Parametric Vertex Enumeration
3714 The parametric vertex enumeration described in this section
3715 is mainly intended to be used internally and by the C<barvinok>
3718 #include <isl/vertices.h>
3719 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3720 __isl_keep isl_basic_set *bset);
3722 The function C<isl_basic_set_compute_vertices> performs the
3723 actual computation of the parametric vertices and the chamber
3724 decomposition and store the result in an C<isl_vertices> object.
3725 This information can be queried by either iterating over all
3726 the vertices or iterating over all the chambers or cells
3727 and then iterating over all vertices that are active on the chamber.
3729 int isl_vertices_foreach_vertex(
3730 __isl_keep isl_vertices *vertices,
3731 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3734 int isl_vertices_foreach_cell(
3735 __isl_keep isl_vertices *vertices,
3736 int (*fn)(__isl_take isl_cell *cell, void *user),
3738 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3739 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3742 Other operations that can be performed on an C<isl_vertices> object are
3745 isl_ctx *isl_vertices_get_ctx(
3746 __isl_keep isl_vertices *vertices);
3747 int isl_vertices_get_n_vertices(
3748 __isl_keep isl_vertices *vertices);
3749 void isl_vertices_free(__isl_take isl_vertices *vertices);
3751 Vertices can be inspected and destroyed using the following functions.
3753 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3754 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3755 __isl_give isl_basic_set *isl_vertex_get_domain(
3756 __isl_keep isl_vertex *vertex);
3757 __isl_give isl_basic_set *isl_vertex_get_expr(
3758 __isl_keep isl_vertex *vertex);
3759 void isl_vertex_free(__isl_take isl_vertex *vertex);
3761 C<isl_vertex_get_expr> returns a singleton parametric set describing
3762 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3764 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3765 B<rational> basic sets, so they should mainly be used for inspection
3766 and should not be mixed with integer sets.
3768 Chambers can be inspected and destroyed using the following functions.
3770 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3771 __isl_give isl_basic_set *isl_cell_get_domain(
3772 __isl_keep isl_cell *cell);
3773 void isl_cell_free(__isl_take isl_cell *cell);
3777 Although C<isl> is mainly meant to be used as a library,
3778 it also contains some basic applications that use some
3779 of the functionality of C<isl>.
3780 The input may be specified in either the L<isl format>
3781 or the L<PolyLib format>.
3783 =head2 C<isl_polyhedron_sample>
3785 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3786 an integer element of the polyhedron, if there is any.
3787 The first column in the output is the denominator and is always
3788 equal to 1. If the polyhedron contains no integer points,
3789 then a vector of length zero is printed.
3793 C<isl_pip> takes the same input as the C<example> program
3794 from the C<piplib> distribution, i.e., a set of constraints
3795 on the parameters, a line containing only -1 and finally a set
3796 of constraints on a parametric polyhedron.
3797 The coefficients of the parameters appear in the last columns
3798 (but before the final constant column).
3799 The output is the lexicographic minimum of the parametric polyhedron.
3800 As C<isl> currently does not have its own output format, the output
3801 is just a dump of the internal state.
3803 =head2 C<isl_polyhedron_minimize>
3805 C<isl_polyhedron_minimize> computes the minimum of some linear
3806 or affine objective function over the integer points in a polyhedron.
3807 If an affine objective function
3808 is given, then the constant should appear in the last column.
3810 =head2 C<isl_polytope_scan>
3812 Given a polytope, C<isl_polytope_scan> prints
3813 all integer points in the polytope.