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);
601 __isl_give isl_space *isl_multi_aff_get_space(
602 __isl_keep isl_multi_aff *maff);
603 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
604 __isl_keep isl_pw_multi_aff *pma);
605 __isl_give isl_space *isl_pw_multi_aff_get_space(
606 __isl_keep isl_pw_multi_aff *pma);
608 #include <isl/point.h>
609 __isl_give isl_space *isl_point_get_space(
610 __isl_keep isl_point *pnt);
612 The identifiers or names of the individual dimensions may be set or read off
613 using the following functions.
615 #include <isl/space.h>
616 __isl_give isl_space *isl_space_set_dim_id(
617 __isl_take isl_space *space,
618 enum isl_dim_type type, unsigned pos,
619 __isl_take isl_id *id);
620 int isl_space_has_dim_id(__isl_keep isl_space *space,
621 enum isl_dim_type type, unsigned pos);
622 __isl_give isl_id *isl_space_get_dim_id(
623 __isl_keep isl_space *space,
624 enum isl_dim_type type, unsigned pos);
625 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
626 enum isl_dim_type type, unsigned pos,
627 __isl_keep const char *name);
628 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
629 enum isl_dim_type type, unsigned pos);
631 Note that C<isl_space_get_name> returns a pointer to some internal
632 data structure, so the result can only be used while the
633 corresponding C<isl_space> is alive.
634 Also note that every function that operates on two sets or relations
635 requires that both arguments have the same parameters. This also
636 means that if one of the arguments has named parameters, then the
637 other needs to have named parameters too and the names need to match.
638 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
639 arguments may have different parameters (as long as they are named),
640 in which case the result will have as parameters the union of the parameters of
643 Given the identifier or name of a dimension (typically a parameter),
644 its position can be obtained from the following function.
646 #include <isl/space.h>
647 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
648 enum isl_dim_type type, __isl_keep isl_id *id);
649 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
650 enum isl_dim_type type, const char *name);
652 The identifiers or names of entire spaces may be set or read off
653 using the following functions.
655 #include <isl/space.h>
656 __isl_give isl_space *isl_space_set_tuple_id(
657 __isl_take isl_space *space,
658 enum isl_dim_type type, __isl_take isl_id *id);
659 __isl_give isl_space *isl_space_reset_tuple_id(
660 __isl_take isl_space *space, enum isl_dim_type type);
661 int isl_space_has_tuple_id(__isl_keep isl_space *space,
662 enum isl_dim_type type);
663 __isl_give isl_id *isl_space_get_tuple_id(
664 __isl_keep isl_space *space, enum isl_dim_type type);
665 __isl_give isl_space *isl_space_set_tuple_name(
666 __isl_take isl_space *space,
667 enum isl_dim_type type, const char *s);
668 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
669 enum isl_dim_type type);
671 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
672 or C<isl_dim_set>. As with C<isl_space_get_name>,
673 the C<isl_space_get_tuple_name> function returns a pointer to some internal
675 Binary operations require the corresponding spaces of their arguments
676 to have the same name.
678 Spaces can be nested. In particular, the domain of a set or
679 the domain or range of a relation can be a nested relation.
680 The following functions can be used to construct and deconstruct
683 #include <isl/space.h>
684 int isl_space_is_wrapping(__isl_keep isl_space *space);
685 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
686 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
688 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
689 be the space of a set, while that of
690 C<isl_space_wrap> should be the space of a relation.
691 Conversely, the output of C<isl_space_unwrap> is the space
692 of a relation, while that of C<isl_space_wrap> is the space of a set.
694 Spaces can be created from other spaces
695 using the following functions.
697 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
698 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
699 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
700 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
701 __isl_give isl_space *isl_space_params(
702 __isl_take isl_space *space);
703 __isl_give isl_space *isl_space_set_from_params(
704 __isl_take isl_space *space);
705 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
706 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
707 __isl_take isl_space *right);
708 __isl_give isl_space *isl_space_align_params(
709 __isl_take isl_space *space1, __isl_take isl_space *space2)
710 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
711 enum isl_dim_type type, unsigned pos, unsigned n);
712 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
713 enum isl_dim_type type, unsigned n);
714 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
715 enum isl_dim_type type, unsigned first, unsigned n);
716 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
717 enum isl_dim_type dst_type, unsigned dst_pos,
718 enum isl_dim_type src_type, unsigned src_pos,
720 __isl_give isl_space *isl_space_map_from_set(
721 __isl_take isl_space *space);
722 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
724 Note that if dimensions are added or removed from a space, then
725 the name and the internal structure are lost.
729 A local space is essentially a space with
730 zero or more existentially quantified variables.
731 The local space of a basic set or relation can be obtained
732 using the following functions.
735 __isl_give isl_local_space *isl_basic_set_get_local_space(
736 __isl_keep isl_basic_set *bset);
739 __isl_give isl_local_space *isl_basic_map_get_local_space(
740 __isl_keep isl_basic_map *bmap);
742 A new local space can be created from a space using
744 #include <isl/local_space.h>
745 __isl_give isl_local_space *isl_local_space_from_space(
746 __isl_take isl_space *space);
748 They can be inspected, modified, copied and freed using the following functions.
750 #include <isl/local_space.h>
751 isl_ctx *isl_local_space_get_ctx(
752 __isl_keep isl_local_space *ls);
753 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
754 int isl_local_space_dim(__isl_keep isl_local_space *ls,
755 enum isl_dim_type type);
756 const char *isl_local_space_get_dim_name(
757 __isl_keep isl_local_space *ls,
758 enum isl_dim_type type, unsigned pos);
759 __isl_give isl_local_space *isl_local_space_set_dim_name(
760 __isl_take isl_local_space *ls,
761 enum isl_dim_type type, unsigned pos, const char *s);
762 __isl_give isl_local_space *isl_local_space_set_dim_id(
763 __isl_take isl_local_space *ls,
764 enum isl_dim_type type, unsigned pos,
765 __isl_take isl_id *id);
766 __isl_give isl_space *isl_local_space_get_space(
767 __isl_keep isl_local_space *ls);
768 __isl_give isl_aff *isl_local_space_get_div(
769 __isl_keep isl_local_space *ls, int pos);
770 __isl_give isl_local_space *isl_local_space_copy(
771 __isl_keep isl_local_space *ls);
772 void *isl_local_space_free(__isl_take isl_local_space *ls);
774 Two local spaces can be compared using
776 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
777 __isl_keep isl_local_space *ls2);
779 Local spaces can be created from other local spaces
780 using the following functions.
782 __isl_give isl_local_space *isl_local_space_domain(
783 __isl_take isl_local_space *ls);
784 __isl_give isl_local_space *isl_local_space_from_domain(
785 __isl_take isl_local_space *ls);
786 __isl_give isl_local_space *isl_local_space_add_dims(
787 __isl_take isl_local_space *ls,
788 enum isl_dim_type type, unsigned n);
789 __isl_give isl_local_space *isl_local_space_insert_dims(
790 __isl_take isl_local_space *ls,
791 enum isl_dim_type type, unsigned first, unsigned n);
792 __isl_give isl_local_space *isl_local_space_drop_dims(
793 __isl_take isl_local_space *ls,
794 enum isl_dim_type type, unsigned first, unsigned n);
796 =head2 Input and Output
798 C<isl> supports its own input/output format, which is similar
799 to the C<Omega> format, but also supports the C<PolyLib> format
804 The C<isl> format is similar to that of C<Omega>, but has a different
805 syntax for describing the parameters and allows for the definition
806 of an existentially quantified variable as the integer division
807 of an affine expression.
808 For example, the set of integers C<i> between C<0> and C<n>
809 such that C<i % 10 <= 6> can be described as
811 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
814 A set or relation can have several disjuncts, separated
815 by the keyword C<or>. Each disjunct is either a conjunction
816 of constraints or a projection (C<exists>) of a conjunction
817 of constraints. The constraints are separated by the keyword
820 =head3 C<PolyLib> format
822 If the represented set is a union, then the first line
823 contains a single number representing the number of disjuncts.
824 Otherwise, a line containing the number C<1> is optional.
826 Each disjunct is represented by a matrix of constraints.
827 The first line contains two numbers representing
828 the number of rows and columns,
829 where the number of rows is equal to the number of constraints
830 and the number of columns is equal to two plus the number of variables.
831 The following lines contain the actual rows of the constraint matrix.
832 In each row, the first column indicates whether the constraint
833 is an equality (C<0>) or inequality (C<1>). The final column
834 corresponds to the constant term.
836 If the set is parametric, then the coefficients of the parameters
837 appear in the last columns before the constant column.
838 The coefficients of any existentially quantified variables appear
839 between those of the set variables and those of the parameters.
841 =head3 Extended C<PolyLib> format
843 The extended C<PolyLib> format is nearly identical to the
844 C<PolyLib> format. The only difference is that the line
845 containing the number of rows and columns of a constraint matrix
846 also contains four additional numbers:
847 the number of output dimensions, the number of input dimensions,
848 the number of local dimensions (i.e., the number of existentially
849 quantified variables) and the number of parameters.
850 For sets, the number of ``output'' dimensions is equal
851 to the number of set dimensions, while the number of ``input''
857 __isl_give isl_basic_set *isl_basic_set_read_from_file(
858 isl_ctx *ctx, FILE *input);
859 __isl_give isl_basic_set *isl_basic_set_read_from_str(
860 isl_ctx *ctx, const char *str);
861 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
863 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
867 __isl_give isl_basic_map *isl_basic_map_read_from_file(
868 isl_ctx *ctx, FILE *input);
869 __isl_give isl_basic_map *isl_basic_map_read_from_str(
870 isl_ctx *ctx, const char *str);
871 __isl_give isl_map *isl_map_read_from_file(
872 isl_ctx *ctx, FILE *input);
873 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
876 #include <isl/union_set.h>
877 __isl_give isl_union_set *isl_union_set_read_from_file(
878 isl_ctx *ctx, FILE *input);
879 __isl_give isl_union_set *isl_union_set_read_from_str(
880 isl_ctx *ctx, const char *str);
882 #include <isl/union_map.h>
883 __isl_give isl_union_map *isl_union_map_read_from_file(
884 isl_ctx *ctx, FILE *input);
885 __isl_give isl_union_map *isl_union_map_read_from_str(
886 isl_ctx *ctx, const char *str);
888 The input format is autodetected and may be either the C<PolyLib> format
889 or the C<isl> format.
893 Before anything can be printed, an C<isl_printer> needs to
896 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
898 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
899 void isl_printer_free(__isl_take isl_printer *printer);
900 __isl_give char *isl_printer_get_str(
901 __isl_keep isl_printer *printer);
903 The behavior of the printer can be modified in various ways
905 __isl_give isl_printer *isl_printer_set_output_format(
906 __isl_take isl_printer *p, int output_format);
907 __isl_give isl_printer *isl_printer_set_indent(
908 __isl_take isl_printer *p, int indent);
909 __isl_give isl_printer *isl_printer_indent(
910 __isl_take isl_printer *p, int indent);
911 __isl_give isl_printer *isl_printer_set_prefix(
912 __isl_take isl_printer *p, const char *prefix);
913 __isl_give isl_printer *isl_printer_set_suffix(
914 __isl_take isl_printer *p, const char *suffix);
916 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
917 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
918 and defaults to C<ISL_FORMAT_ISL>.
919 Each line in the output is indented by C<indent> (set by
920 C<isl_printer_set_indent>) spaces
921 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
922 In the C<PolyLib> format output,
923 the coefficients of the existentially quantified variables
924 appear between those of the set variables and those
926 The function C<isl_printer_indent> increases the indentation
927 by the specified amount (which may be negative).
929 To actually print something, use
932 __isl_give isl_printer *isl_printer_print_basic_set(
933 __isl_take isl_printer *printer,
934 __isl_keep isl_basic_set *bset);
935 __isl_give isl_printer *isl_printer_print_set(
936 __isl_take isl_printer *printer,
937 __isl_keep isl_set *set);
940 __isl_give isl_printer *isl_printer_print_basic_map(
941 __isl_take isl_printer *printer,
942 __isl_keep isl_basic_map *bmap);
943 __isl_give isl_printer *isl_printer_print_map(
944 __isl_take isl_printer *printer,
945 __isl_keep isl_map *map);
947 #include <isl/union_set.h>
948 __isl_give isl_printer *isl_printer_print_union_set(
949 __isl_take isl_printer *p,
950 __isl_keep isl_union_set *uset);
952 #include <isl/union_map.h>
953 __isl_give isl_printer *isl_printer_print_union_map(
954 __isl_take isl_printer *p,
955 __isl_keep isl_union_map *umap);
957 When called on a file printer, the following function flushes
958 the file. When called on a string printer, the buffer is cleared.
960 __isl_give isl_printer *isl_printer_flush(
961 __isl_take isl_printer *p);
963 =head2 Creating New Sets and Relations
965 C<isl> has functions for creating some standard sets and relations.
969 =item * Empty sets and relations
971 __isl_give isl_basic_set *isl_basic_set_empty(
972 __isl_take isl_space *space);
973 __isl_give isl_basic_map *isl_basic_map_empty(
974 __isl_take isl_space *space);
975 __isl_give isl_set *isl_set_empty(
976 __isl_take isl_space *space);
977 __isl_give isl_map *isl_map_empty(
978 __isl_take isl_space *space);
979 __isl_give isl_union_set *isl_union_set_empty(
980 __isl_take isl_space *space);
981 __isl_give isl_union_map *isl_union_map_empty(
982 __isl_take isl_space *space);
984 For C<isl_union_set>s and C<isl_union_map>s, the space
985 is only used to specify the parameters.
987 =item * Universe sets and relations
989 __isl_give isl_basic_set *isl_basic_set_universe(
990 __isl_take isl_space *space);
991 __isl_give isl_basic_map *isl_basic_map_universe(
992 __isl_take isl_space *space);
993 __isl_give isl_set *isl_set_universe(
994 __isl_take isl_space *space);
995 __isl_give isl_map *isl_map_universe(
996 __isl_take isl_space *space);
997 __isl_give isl_union_set *isl_union_set_universe(
998 __isl_take isl_union_set *uset);
999 __isl_give isl_union_map *isl_union_map_universe(
1000 __isl_take isl_union_map *umap);
1002 The sets and relations constructed by the functions above
1003 contain all integer values, while those constructed by the
1004 functions below only contain non-negative values.
1006 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1007 __isl_take isl_space *space);
1008 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1009 __isl_take isl_space *space);
1010 __isl_give isl_set *isl_set_nat_universe(
1011 __isl_take isl_space *space);
1012 __isl_give isl_map *isl_map_nat_universe(
1013 __isl_take isl_space *space);
1015 =item * Identity relations
1017 __isl_give isl_basic_map *isl_basic_map_identity(
1018 __isl_take isl_space *space);
1019 __isl_give isl_map *isl_map_identity(
1020 __isl_take isl_space *space);
1022 The number of input and output dimensions in C<space> needs
1025 =item * Lexicographic order
1027 __isl_give isl_map *isl_map_lex_lt(
1028 __isl_take isl_space *set_space);
1029 __isl_give isl_map *isl_map_lex_le(
1030 __isl_take isl_space *set_space);
1031 __isl_give isl_map *isl_map_lex_gt(
1032 __isl_take isl_space *set_space);
1033 __isl_give isl_map *isl_map_lex_ge(
1034 __isl_take isl_space *set_space);
1035 __isl_give isl_map *isl_map_lex_lt_first(
1036 __isl_take isl_space *space, unsigned n);
1037 __isl_give isl_map *isl_map_lex_le_first(
1038 __isl_take isl_space *space, unsigned n);
1039 __isl_give isl_map *isl_map_lex_gt_first(
1040 __isl_take isl_space *space, unsigned n);
1041 __isl_give isl_map *isl_map_lex_ge_first(
1042 __isl_take isl_space *space, unsigned n);
1044 The first four functions take a space for a B<set>
1045 and return relations that express that the elements in the domain
1046 are lexicographically less
1047 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1048 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1049 than the elements in the range.
1050 The last four functions take a space for a map
1051 and return relations that express that the first C<n> dimensions
1052 in the domain are lexicographically less
1053 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1054 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1055 than the first C<n> dimensions in the range.
1059 A basic set or relation can be converted to a set or relation
1060 using the following functions.
1062 __isl_give isl_set *isl_set_from_basic_set(
1063 __isl_take isl_basic_set *bset);
1064 __isl_give isl_map *isl_map_from_basic_map(
1065 __isl_take isl_basic_map *bmap);
1067 Sets and relations can be converted to union sets and relations
1068 using the following functions.
1070 __isl_give isl_union_map *isl_union_map_from_map(
1071 __isl_take isl_map *map);
1072 __isl_give isl_union_set *isl_union_set_from_set(
1073 __isl_take isl_set *set);
1075 The inverse conversions below can only be used if the input
1076 union set or relation is known to contain elements in exactly one
1079 __isl_give isl_set *isl_set_from_union_set(
1080 __isl_take isl_union_set *uset);
1081 __isl_give isl_map *isl_map_from_union_map(
1082 __isl_take isl_union_map *umap);
1084 A zero-dimensional set can be constructed on a given parameter domain
1085 using the following function.
1087 __isl_give isl_set *isl_set_from_params(
1088 __isl_take isl_set *set);
1090 Sets and relations can be copied and freed again using the following
1093 __isl_give isl_basic_set *isl_basic_set_copy(
1094 __isl_keep isl_basic_set *bset);
1095 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1096 __isl_give isl_union_set *isl_union_set_copy(
1097 __isl_keep isl_union_set *uset);
1098 __isl_give isl_basic_map *isl_basic_map_copy(
1099 __isl_keep isl_basic_map *bmap);
1100 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1101 __isl_give isl_union_map *isl_union_map_copy(
1102 __isl_keep isl_union_map *umap);
1103 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1104 void isl_set_free(__isl_take isl_set *set);
1105 void *isl_union_set_free(__isl_take isl_union_set *uset);
1106 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1107 void isl_map_free(__isl_take isl_map *map);
1108 void *isl_union_map_free(__isl_take isl_union_map *umap);
1110 Other sets and relations can be constructed by starting
1111 from a universe set or relation, adding equality and/or
1112 inequality constraints and then projecting out the
1113 existentially quantified variables, if any.
1114 Constraints can be constructed, manipulated and
1115 added to (or removed from) (basic) sets and relations
1116 using the following functions.
1118 #include <isl/constraint.h>
1119 __isl_give isl_constraint *isl_equality_alloc(
1120 __isl_take isl_local_space *ls);
1121 __isl_give isl_constraint *isl_inequality_alloc(
1122 __isl_take isl_local_space *ls);
1123 __isl_give isl_constraint *isl_constraint_set_constant(
1124 __isl_take isl_constraint *constraint, isl_int v);
1125 __isl_give isl_constraint *isl_constraint_set_constant_si(
1126 __isl_take isl_constraint *constraint, int v);
1127 __isl_give isl_constraint *isl_constraint_set_coefficient(
1128 __isl_take isl_constraint *constraint,
1129 enum isl_dim_type type, int pos, isl_int v);
1130 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1131 __isl_take isl_constraint *constraint,
1132 enum isl_dim_type type, int pos, int v);
1133 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1134 __isl_take isl_basic_map *bmap,
1135 __isl_take isl_constraint *constraint);
1136 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1137 __isl_take isl_basic_set *bset,
1138 __isl_take isl_constraint *constraint);
1139 __isl_give isl_map *isl_map_add_constraint(
1140 __isl_take isl_map *map,
1141 __isl_take isl_constraint *constraint);
1142 __isl_give isl_set *isl_set_add_constraint(
1143 __isl_take isl_set *set,
1144 __isl_take isl_constraint *constraint);
1145 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1146 __isl_take isl_basic_set *bset,
1147 __isl_take isl_constraint *constraint);
1149 For example, to create a set containing the even integers
1150 between 10 and 42, you would use the following code.
1153 isl_local_space *ls;
1155 isl_basic_set *bset;
1157 space = isl_space_set_alloc(ctx, 0, 2);
1158 bset = isl_basic_set_universe(isl_space_copy(space));
1159 ls = isl_local_space_from_space(space);
1161 c = isl_equality_alloc(isl_local_space_copy(ls));
1162 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1163 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1164 bset = isl_basic_set_add_constraint(bset, c);
1166 c = isl_inequality_alloc(isl_local_space_copy(ls));
1167 c = isl_constraint_set_constant_si(c, -10);
1168 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1169 bset = isl_basic_set_add_constraint(bset, c);
1171 c = isl_inequality_alloc(ls);
1172 c = isl_constraint_set_constant_si(c, 42);
1173 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1174 bset = isl_basic_set_add_constraint(bset, c);
1176 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1180 isl_basic_set *bset;
1181 bset = isl_basic_set_read_from_str(ctx,
1182 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1184 A basic set or relation can also be constructed from two matrices
1185 describing the equalities and the inequalities.
1187 __isl_give isl_basic_set *isl_basic_set_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);
1193 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1194 __isl_take isl_space *space,
1195 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1196 enum isl_dim_type c1,
1197 enum isl_dim_type c2, enum isl_dim_type c3,
1198 enum isl_dim_type c4, enum isl_dim_type c5);
1200 The C<isl_dim_type> arguments indicate the order in which
1201 different kinds of variables appear in the input matrices
1202 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1203 C<isl_dim_set> and C<isl_dim_div> for sets and
1204 of C<isl_dim_cst>, C<isl_dim_param>,
1205 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1207 A (basic) set or relation can also be constructed from a (piecewise)
1208 (multiple) affine expression
1209 or a list of affine expressions
1210 (See L<"Piecewise Quasi Affine Expressions"> and
1211 L<"Piecewise Multiple Quasi Affine Expressions">).
1213 __isl_give isl_basic_map *isl_basic_map_from_aff(
1214 __isl_take isl_aff *aff);
1215 __isl_give isl_set *isl_set_from_pw_aff(
1216 __isl_take isl_pw_aff *pwaff);
1217 __isl_give isl_map *isl_map_from_pw_aff(
1218 __isl_take isl_pw_aff *pwaff);
1219 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1220 __isl_take isl_space *domain_space,
1221 __isl_take isl_aff_list *list);
1222 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1223 __isl_take isl_multi_aff *maff)
1224 __isl_give isl_set *isl_set_from_pw_multi_aff(
1225 __isl_take isl_pw_multi_aff *pma);
1226 __isl_give isl_map *isl_map_from_pw_multi_aff(
1227 __isl_take isl_pw_multi_aff *pma);
1229 The C<domain_dim> argument describes the domain of the resulting
1230 basic relation. It is required because the C<list> may consist
1231 of zero affine expressions.
1233 =head2 Inspecting Sets and Relations
1235 Usually, the user should not have to care about the actual constraints
1236 of the sets and maps, but should instead apply the abstract operations
1237 explained in the following sections.
1238 Occasionally, however, it may be required to inspect the individual
1239 coefficients of the constraints. This section explains how to do so.
1240 In these cases, it may also be useful to have C<isl> compute
1241 an explicit representation of the existentially quantified variables.
1243 __isl_give isl_set *isl_set_compute_divs(
1244 __isl_take isl_set *set);
1245 __isl_give isl_map *isl_map_compute_divs(
1246 __isl_take isl_map *map);
1247 __isl_give isl_union_set *isl_union_set_compute_divs(
1248 __isl_take isl_union_set *uset);
1249 __isl_give isl_union_map *isl_union_map_compute_divs(
1250 __isl_take isl_union_map *umap);
1252 This explicit representation defines the existentially quantified
1253 variables as integer divisions of the other variables, possibly
1254 including earlier existentially quantified variables.
1255 An explicitly represented existentially quantified variable therefore
1256 has a unique value when the values of the other variables are known.
1257 If, furthermore, the same existentials, i.e., existentials
1258 with the same explicit representations, should appear in the
1259 same order in each of the disjuncts of a set or map, then the user should call
1260 either of the following functions.
1262 __isl_give isl_set *isl_set_align_divs(
1263 __isl_take isl_set *set);
1264 __isl_give isl_map *isl_map_align_divs(
1265 __isl_take isl_map *map);
1267 Alternatively, the existentially quantified variables can be removed
1268 using the following functions, which compute an overapproximation.
1270 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1271 __isl_take isl_basic_set *bset);
1272 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1273 __isl_take isl_basic_map *bmap);
1274 __isl_give isl_set *isl_set_remove_divs(
1275 __isl_take isl_set *set);
1276 __isl_give isl_map *isl_map_remove_divs(
1277 __isl_take isl_map *map);
1279 To iterate over all the sets or maps in a union set or map, use
1281 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1282 int (*fn)(__isl_take isl_set *set, void *user),
1284 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1285 int (*fn)(__isl_take isl_map *map, void *user),
1288 The number of sets or maps in a union set or map can be obtained
1291 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1292 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1294 To extract the set or map in a given space from a union, use
1296 __isl_give isl_set *isl_union_set_extract_set(
1297 __isl_keep isl_union_set *uset,
1298 __isl_take isl_space *space);
1299 __isl_give isl_map *isl_union_map_extract_map(
1300 __isl_keep isl_union_map *umap,
1301 __isl_take isl_space *space);
1303 To iterate over all the basic sets or maps in a set or map, use
1305 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1306 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1308 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1309 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1312 The callback function C<fn> should return 0 if successful and
1313 -1 if an error occurs. In the latter case, or if any other error
1314 occurs, the above functions will return -1.
1316 It should be noted that C<isl> does not guarantee that
1317 the basic sets or maps passed to C<fn> are disjoint.
1318 If this is required, then the user should call one of
1319 the following functions first.
1321 __isl_give isl_set *isl_set_make_disjoint(
1322 __isl_take isl_set *set);
1323 __isl_give isl_map *isl_map_make_disjoint(
1324 __isl_take isl_map *map);
1326 The number of basic sets in a set can be obtained
1329 int isl_set_n_basic_set(__isl_keep isl_set *set);
1331 To iterate over the constraints of a basic set or map, use
1333 #include <isl/constraint.h>
1335 int isl_basic_map_foreach_constraint(
1336 __isl_keep isl_basic_map *bmap,
1337 int (*fn)(__isl_take isl_constraint *c, void *user),
1339 void *isl_constraint_free(__isl_take isl_constraint *c);
1341 Again, the callback function C<fn> should return 0 if successful and
1342 -1 if an error occurs. In the latter case, or if any other error
1343 occurs, the above functions will return -1.
1344 The constraint C<c> represents either an equality or an inequality.
1345 Use the following function to find out whether a constraint
1346 represents an equality. If not, it represents an inequality.
1348 int isl_constraint_is_equality(
1349 __isl_keep isl_constraint *constraint);
1351 The coefficients of the constraints can be inspected using
1352 the following functions.
1354 void isl_constraint_get_constant(
1355 __isl_keep isl_constraint *constraint, isl_int *v);
1356 void isl_constraint_get_coefficient(
1357 __isl_keep isl_constraint *constraint,
1358 enum isl_dim_type type, int pos, isl_int *v);
1359 int isl_constraint_involves_dims(
1360 __isl_keep isl_constraint *constraint,
1361 enum isl_dim_type type, unsigned first, unsigned n);
1363 The explicit representations of the existentially quantified
1364 variables can be inspected using the following function.
1365 Note that the user is only allowed to use this function
1366 if the inspected set or map is the result of a call
1367 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1368 The existentially quantified variable is equal to the floor
1369 of the returned affine expression. The affine expression
1370 itself can be inspected using the functions in
1371 L<"Piecewise Quasi Affine Expressions">.
1373 __isl_give isl_aff *isl_constraint_get_div(
1374 __isl_keep isl_constraint *constraint, int pos);
1376 To obtain the constraints of a basic set or map in matrix
1377 form, use the following functions.
1379 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1380 __isl_keep isl_basic_set *bset,
1381 enum isl_dim_type c1, enum isl_dim_type c2,
1382 enum isl_dim_type c3, enum isl_dim_type c4);
1383 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1384 __isl_keep isl_basic_set *bset,
1385 enum isl_dim_type c1, enum isl_dim_type c2,
1386 enum isl_dim_type c3, enum isl_dim_type c4);
1387 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1388 __isl_keep isl_basic_map *bmap,
1389 enum isl_dim_type c1,
1390 enum isl_dim_type c2, enum isl_dim_type c3,
1391 enum isl_dim_type c4, enum isl_dim_type c5);
1392 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1393 __isl_keep isl_basic_map *bmap,
1394 enum isl_dim_type c1,
1395 enum isl_dim_type c2, enum isl_dim_type c3,
1396 enum isl_dim_type c4, enum isl_dim_type c5);
1398 The C<isl_dim_type> arguments dictate the order in which
1399 different kinds of variables appear in the resulting matrix
1400 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1401 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1403 The number of parameters, input, output or set dimensions can
1404 be obtained using the following functions.
1406 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1407 enum isl_dim_type type);
1408 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1409 enum isl_dim_type type);
1410 unsigned isl_set_dim(__isl_keep isl_set *set,
1411 enum isl_dim_type type);
1412 unsigned isl_map_dim(__isl_keep isl_map *map,
1413 enum isl_dim_type type);
1415 To check whether the description of a set or relation depends
1416 on one or more given dimensions, it is not necessary to iterate over all
1417 constraints. Instead the following functions can be used.
1419 int isl_basic_set_involves_dims(
1420 __isl_keep isl_basic_set *bset,
1421 enum isl_dim_type type, unsigned first, unsigned n);
1422 int isl_set_involves_dims(__isl_keep isl_set *set,
1423 enum isl_dim_type type, unsigned first, unsigned n);
1424 int isl_basic_map_involves_dims(
1425 __isl_keep isl_basic_map *bmap,
1426 enum isl_dim_type type, unsigned first, unsigned n);
1427 int isl_map_involves_dims(__isl_keep isl_map *map,
1428 enum isl_dim_type type, unsigned first, unsigned n);
1430 Similarly, the following functions can be used to check whether
1431 a given dimension is involved in any lower or upper bound.
1433 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1434 enum isl_dim_type type, unsigned pos);
1435 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1436 enum isl_dim_type type, unsigned pos);
1438 The identifiers or names of the domain and range spaces of a set
1439 or relation can be read off or set using the following functions.
1441 __isl_give isl_set *isl_set_set_tuple_id(
1442 __isl_take isl_set *set, __isl_take isl_id *id);
1443 __isl_give isl_set *isl_set_reset_tuple_id(
1444 __isl_take isl_set *set);
1445 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1446 __isl_give isl_id *isl_set_get_tuple_id(
1447 __isl_keep isl_set *set);
1448 __isl_give isl_map *isl_map_set_tuple_id(
1449 __isl_take isl_map *map, enum isl_dim_type type,
1450 __isl_take isl_id *id);
1451 __isl_give isl_map *isl_map_reset_tuple_id(
1452 __isl_take isl_map *map, enum isl_dim_type type);
1453 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1454 enum isl_dim_type type);
1455 __isl_give isl_id *isl_map_get_tuple_id(
1456 __isl_keep isl_map *map, enum isl_dim_type type);
1458 const char *isl_basic_set_get_tuple_name(
1459 __isl_keep isl_basic_set *bset);
1460 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1461 __isl_take isl_basic_set *set, const char *s);
1462 const char *isl_set_get_tuple_name(
1463 __isl_keep isl_set *set);
1464 const char *isl_basic_map_get_tuple_name(
1465 __isl_keep isl_basic_map *bmap,
1466 enum isl_dim_type type);
1467 const char *isl_map_get_tuple_name(
1468 __isl_keep isl_map *map,
1469 enum isl_dim_type type);
1471 As with C<isl_space_get_tuple_name>, the value returned points to
1472 an internal data structure.
1473 The identifiers, positions or names of individual dimensions can be
1474 read off using the following functions.
1476 __isl_give isl_set *isl_set_set_dim_id(
1477 __isl_take isl_set *set, enum isl_dim_type type,
1478 unsigned pos, __isl_take isl_id *id);
1479 int isl_set_has_dim_id(__isl_keep isl_set *set,
1480 enum isl_dim_type type, unsigned pos);
1481 __isl_give isl_id *isl_set_get_dim_id(
1482 __isl_keep isl_set *set, enum isl_dim_type type,
1484 int isl_basic_map_has_dim_id(
1485 __isl_keep isl_basic_map *bmap,
1486 enum isl_dim_type type, unsigned pos);
1487 __isl_give isl_map *isl_map_set_dim_id(
1488 __isl_take isl_map *map, enum isl_dim_type type,
1489 unsigned pos, __isl_take isl_id *id);
1490 int isl_map_has_dim_id(__isl_keep isl_map *map,
1491 enum isl_dim_type type, unsigned pos);
1492 __isl_give isl_id *isl_map_get_dim_id(
1493 __isl_keep isl_map *map, enum isl_dim_type type,
1496 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1497 enum isl_dim_type type, __isl_keep isl_id *id);
1498 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1499 enum isl_dim_type type, __isl_keep isl_id *id);
1500 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1501 enum isl_dim_type type, const char *name);
1503 const char *isl_constraint_get_dim_name(
1504 __isl_keep isl_constraint *constraint,
1505 enum isl_dim_type type, unsigned pos);
1506 const char *isl_basic_set_get_dim_name(
1507 __isl_keep isl_basic_set *bset,
1508 enum isl_dim_type type, unsigned pos);
1509 const char *isl_set_get_dim_name(
1510 __isl_keep isl_set *set,
1511 enum isl_dim_type type, unsigned pos);
1512 const char *isl_basic_map_get_dim_name(
1513 __isl_keep isl_basic_map *bmap,
1514 enum isl_dim_type type, unsigned pos);
1515 const char *isl_map_get_dim_name(
1516 __isl_keep isl_map *map,
1517 enum isl_dim_type type, unsigned pos);
1519 These functions are mostly useful to obtain the identifiers, positions
1520 or names of the parameters. Identifiers of individual dimensions are
1521 essentially only useful for printing. They are ignored by all other
1522 operations and may not be preserved across those operations.
1526 =head3 Unary Properties
1532 The following functions test whether the given set or relation
1533 contains any integer points. The ``plain'' variants do not perform
1534 any computations, but simply check if the given set or relation
1535 is already known to be empty.
1537 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1538 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1539 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1540 int isl_set_is_empty(__isl_keep isl_set *set);
1541 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1542 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1543 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1544 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1545 int isl_map_is_empty(__isl_keep isl_map *map);
1546 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1548 =item * Universality
1550 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1551 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1552 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1554 =item * Single-valuedness
1556 int isl_map_is_single_valued(__isl_keep isl_map *map);
1557 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1561 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1562 int isl_map_is_injective(__isl_keep isl_map *map);
1563 int isl_union_map_plain_is_injective(
1564 __isl_keep isl_union_map *umap);
1565 int isl_union_map_is_injective(
1566 __isl_keep isl_union_map *umap);
1570 int isl_map_is_bijective(__isl_keep isl_map *map);
1571 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1575 int isl_basic_map_plain_is_fixed(
1576 __isl_keep isl_basic_map *bmap,
1577 enum isl_dim_type type, unsigned pos,
1579 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1580 enum isl_dim_type type, unsigned pos,
1582 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1583 enum isl_dim_type type, unsigned pos,
1586 Check if the relation obviously lies on a hyperplane where the given dimension
1587 has a fixed value and if so, return that value in C<*val>.
1591 To check whether a set is a parameter domain, use this function:
1593 int isl_set_is_params(__isl_keep isl_set *set);
1597 The following functions check whether the domain of the given
1598 (basic) set is a wrapped relation.
1600 int isl_basic_set_is_wrapping(
1601 __isl_keep isl_basic_set *bset);
1602 int isl_set_is_wrapping(__isl_keep isl_set *set);
1604 =item * Internal Product
1606 int isl_basic_map_can_zip(
1607 __isl_keep isl_basic_map *bmap);
1608 int isl_map_can_zip(__isl_keep isl_map *map);
1610 Check whether the product of domain and range of the given relation
1612 i.e., whether both domain and range are nested relations.
1616 =head3 Binary Properties
1622 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1623 __isl_keep isl_set *set2);
1624 int isl_set_is_equal(__isl_keep isl_set *set1,
1625 __isl_keep isl_set *set2);
1626 int isl_union_set_is_equal(
1627 __isl_keep isl_union_set *uset1,
1628 __isl_keep isl_union_set *uset2);
1629 int isl_basic_map_is_equal(
1630 __isl_keep isl_basic_map *bmap1,
1631 __isl_keep isl_basic_map *bmap2);
1632 int isl_map_is_equal(__isl_keep isl_map *map1,
1633 __isl_keep isl_map *map2);
1634 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1635 __isl_keep isl_map *map2);
1636 int isl_union_map_is_equal(
1637 __isl_keep isl_union_map *umap1,
1638 __isl_keep isl_union_map *umap2);
1640 =item * Disjointness
1642 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1643 __isl_keep isl_set *set2);
1647 int isl_set_is_subset(__isl_keep isl_set *set1,
1648 __isl_keep isl_set *set2);
1649 int isl_set_is_strict_subset(
1650 __isl_keep isl_set *set1,
1651 __isl_keep isl_set *set2);
1652 int isl_union_set_is_subset(
1653 __isl_keep isl_union_set *uset1,
1654 __isl_keep isl_union_set *uset2);
1655 int isl_union_set_is_strict_subset(
1656 __isl_keep isl_union_set *uset1,
1657 __isl_keep isl_union_set *uset2);
1658 int isl_basic_map_is_subset(
1659 __isl_keep isl_basic_map *bmap1,
1660 __isl_keep isl_basic_map *bmap2);
1661 int isl_basic_map_is_strict_subset(
1662 __isl_keep isl_basic_map *bmap1,
1663 __isl_keep isl_basic_map *bmap2);
1664 int isl_map_is_subset(
1665 __isl_keep isl_map *map1,
1666 __isl_keep isl_map *map2);
1667 int isl_map_is_strict_subset(
1668 __isl_keep isl_map *map1,
1669 __isl_keep isl_map *map2);
1670 int isl_union_map_is_subset(
1671 __isl_keep isl_union_map *umap1,
1672 __isl_keep isl_union_map *umap2);
1673 int isl_union_map_is_strict_subset(
1674 __isl_keep isl_union_map *umap1,
1675 __isl_keep isl_union_map *umap2);
1679 =head2 Unary Operations
1685 __isl_give isl_set *isl_set_complement(
1686 __isl_take isl_set *set);
1690 __isl_give isl_basic_map *isl_basic_map_reverse(
1691 __isl_take isl_basic_map *bmap);
1692 __isl_give isl_map *isl_map_reverse(
1693 __isl_take isl_map *map);
1694 __isl_give isl_union_map *isl_union_map_reverse(
1695 __isl_take isl_union_map *umap);
1699 __isl_give isl_basic_set *isl_basic_set_project_out(
1700 __isl_take isl_basic_set *bset,
1701 enum isl_dim_type type, unsigned first, unsigned n);
1702 __isl_give isl_basic_map *isl_basic_map_project_out(
1703 __isl_take isl_basic_map *bmap,
1704 enum isl_dim_type type, unsigned first, unsigned n);
1705 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1706 enum isl_dim_type type, unsigned first, unsigned n);
1707 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1708 enum isl_dim_type type, unsigned first, unsigned n);
1709 __isl_give isl_basic_set *isl_basic_set_params(
1710 __isl_take isl_basic_set *bset);
1711 __isl_give isl_basic_set *isl_basic_map_domain(
1712 __isl_take isl_basic_map *bmap);
1713 __isl_give isl_basic_set *isl_basic_map_range(
1714 __isl_take isl_basic_map *bmap);
1715 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1716 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1717 __isl_give isl_set *isl_map_domain(
1718 __isl_take isl_map *bmap);
1719 __isl_give isl_set *isl_map_range(
1720 __isl_take isl_map *map);
1721 __isl_give isl_union_set *isl_union_map_domain(
1722 __isl_take isl_union_map *umap);
1723 __isl_give isl_union_set *isl_union_map_range(
1724 __isl_take isl_union_map *umap);
1726 __isl_give isl_basic_map *isl_basic_map_domain_map(
1727 __isl_take isl_basic_map *bmap);
1728 __isl_give isl_basic_map *isl_basic_map_range_map(
1729 __isl_take isl_basic_map *bmap);
1730 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1731 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1732 __isl_give isl_union_map *isl_union_map_domain_map(
1733 __isl_take isl_union_map *umap);
1734 __isl_give isl_union_map *isl_union_map_range_map(
1735 __isl_take isl_union_map *umap);
1737 The functions above construct a (basic, regular or union) relation
1738 that maps (a wrapped version of) the input relation to its domain or range.
1742 __isl_give isl_set *isl_set_eliminate(
1743 __isl_take isl_set *set, enum isl_dim_type type,
1744 unsigned first, unsigned n);
1745 __isl_give isl_basic_map *isl_basic_map_eliminate(
1746 __isl_take isl_basic_map *bmap,
1747 enum isl_dim_type type,
1748 unsigned first, unsigned n);
1750 Eliminate the coefficients for the given dimensions from the constraints,
1751 without removing the dimensions.
1755 __isl_give isl_basic_set *isl_basic_set_fix(
1756 __isl_take isl_basic_set *bset,
1757 enum isl_dim_type type, unsigned pos,
1759 __isl_give isl_basic_set *isl_basic_set_fix_si(
1760 __isl_take isl_basic_set *bset,
1761 enum isl_dim_type type, unsigned pos, int value);
1762 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1763 enum isl_dim_type type, unsigned pos,
1765 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1766 enum isl_dim_type type, unsigned pos, int value);
1767 __isl_give isl_basic_map *isl_basic_map_fix_si(
1768 __isl_take isl_basic_map *bmap,
1769 enum isl_dim_type type, unsigned pos, int value);
1770 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1771 enum isl_dim_type type, unsigned pos, int value);
1773 Intersect the set or relation with the hyperplane where the given
1774 dimension has the fixed given value.
1776 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1777 enum isl_dim_type type1, int pos1,
1778 enum isl_dim_type type2, int pos2);
1779 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1780 enum isl_dim_type type1, int pos1,
1781 enum isl_dim_type type2, int pos2);
1783 Intersect the set or relation with the hyperplane where the given
1784 dimensions are equal to each other.
1786 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1787 enum isl_dim_type type1, int pos1,
1788 enum isl_dim_type type2, int pos2);
1790 Intersect the relation with the hyperplane where the given
1791 dimensions have opposite values.
1795 __isl_give isl_map *isl_set_identity(
1796 __isl_take isl_set *set);
1797 __isl_give isl_union_map *isl_union_set_identity(
1798 __isl_take isl_union_set *uset);
1800 Construct an identity relation on the given (union) set.
1804 __isl_give isl_basic_set *isl_basic_map_deltas(
1805 __isl_take isl_basic_map *bmap);
1806 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1807 __isl_give isl_union_set *isl_union_map_deltas(
1808 __isl_take isl_union_map *umap);
1810 These functions return a (basic) set containing the differences
1811 between image elements and corresponding domain elements in the input.
1813 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1814 __isl_take isl_basic_map *bmap);
1815 __isl_give isl_map *isl_map_deltas_map(
1816 __isl_take isl_map *map);
1817 __isl_give isl_union_map *isl_union_map_deltas_map(
1818 __isl_take isl_union_map *umap);
1820 The functions above construct a (basic, regular or union) relation
1821 that maps (a wrapped version of) the input relation to its delta set.
1825 Simplify the representation of a set or relation by trying
1826 to combine pairs of basic sets or relations into a single
1827 basic set or relation.
1829 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1830 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1831 __isl_give isl_union_set *isl_union_set_coalesce(
1832 __isl_take isl_union_set *uset);
1833 __isl_give isl_union_map *isl_union_map_coalesce(
1834 __isl_take isl_union_map *umap);
1836 =item * Detecting equalities
1838 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1839 __isl_take isl_basic_set *bset);
1840 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1841 __isl_take isl_basic_map *bmap);
1842 __isl_give isl_set *isl_set_detect_equalities(
1843 __isl_take isl_set *set);
1844 __isl_give isl_map *isl_map_detect_equalities(
1845 __isl_take isl_map *map);
1846 __isl_give isl_union_set *isl_union_set_detect_equalities(
1847 __isl_take isl_union_set *uset);
1848 __isl_give isl_union_map *isl_union_map_detect_equalities(
1849 __isl_take isl_union_map *umap);
1851 Simplify the representation of a set or relation by detecting implicit
1854 =item * Removing redundant constraints
1856 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1857 __isl_take isl_basic_set *bset);
1858 __isl_give isl_set *isl_set_remove_redundancies(
1859 __isl_take isl_set *set);
1860 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1861 __isl_take isl_basic_map *bmap);
1862 __isl_give isl_map *isl_map_remove_redundancies(
1863 __isl_take isl_map *map);
1867 __isl_give isl_basic_set *isl_set_convex_hull(
1868 __isl_take isl_set *set);
1869 __isl_give isl_basic_map *isl_map_convex_hull(
1870 __isl_take isl_map *map);
1872 If the input set or relation has any existentially quantified
1873 variables, then the result of these operations is currently undefined.
1877 __isl_give isl_basic_set *isl_set_simple_hull(
1878 __isl_take isl_set *set);
1879 __isl_give isl_basic_map *isl_map_simple_hull(
1880 __isl_take isl_map *map);
1881 __isl_give isl_union_map *isl_union_map_simple_hull(
1882 __isl_take isl_union_map *umap);
1884 These functions compute a single basic set or relation
1885 that contains the whole input set or relation.
1886 In particular, the output is described by translates
1887 of the constraints describing the basic sets or relations in the input.
1891 (See \autoref{s:simple hull}.)
1897 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1898 __isl_take isl_basic_set *bset);
1899 __isl_give isl_basic_set *isl_set_affine_hull(
1900 __isl_take isl_set *set);
1901 __isl_give isl_union_set *isl_union_set_affine_hull(
1902 __isl_take isl_union_set *uset);
1903 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1904 __isl_take isl_basic_map *bmap);
1905 __isl_give isl_basic_map *isl_map_affine_hull(
1906 __isl_take isl_map *map);
1907 __isl_give isl_union_map *isl_union_map_affine_hull(
1908 __isl_take isl_union_map *umap);
1910 In case of union sets and relations, the affine hull is computed
1913 =item * Polyhedral hull
1915 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1916 __isl_take isl_set *set);
1917 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1918 __isl_take isl_map *map);
1919 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1920 __isl_take isl_union_set *uset);
1921 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1922 __isl_take isl_union_map *umap);
1924 These functions compute a single basic set or relation
1925 not involving any existentially quantified variables
1926 that contains the whole input set or relation.
1927 In case of union sets and relations, the polyhedral hull is computed
1930 =item * Optimization
1932 #include <isl/ilp.h>
1933 enum isl_lp_result isl_basic_set_max(
1934 __isl_keep isl_basic_set *bset,
1935 __isl_keep isl_aff *obj, isl_int *opt)
1936 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1937 __isl_keep isl_aff *obj, isl_int *opt);
1938 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1939 __isl_keep isl_aff *obj, isl_int *opt);
1941 Compute the minimum or maximum of the integer affine expression C<obj>
1942 over the points in C<set>, returning the result in C<opt>.
1943 The return value may be one of C<isl_lp_error>,
1944 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1946 =item * Parametric optimization
1948 __isl_give isl_pw_aff *isl_set_dim_min(
1949 __isl_take isl_set *set, int pos);
1950 __isl_give isl_pw_aff *isl_set_dim_max(
1951 __isl_take isl_set *set, int pos);
1952 __isl_give isl_pw_aff *isl_map_dim_max(
1953 __isl_take isl_map *map, int pos);
1955 Compute the minimum or maximum of the given set or output dimension
1956 as a function of the parameters (and input dimensions), but independently
1957 of the other set or output dimensions.
1958 For lexicographic optimization, see L<"Lexicographic Optimization">.
1962 The following functions compute either the set of (rational) coefficient
1963 values of valid constraints for the given set or the set of (rational)
1964 values satisfying the constraints with coefficients from the given set.
1965 Internally, these two sets of functions perform essentially the
1966 same operations, except that the set of coefficients is assumed to
1967 be a cone, while the set of values may be any polyhedron.
1968 The current implementation is based on the Farkas lemma and
1969 Fourier-Motzkin elimination, but this may change or be made optional
1970 in future. In particular, future implementations may use different
1971 dualization algorithms or skip the elimination step.
1973 __isl_give isl_basic_set *isl_basic_set_coefficients(
1974 __isl_take isl_basic_set *bset);
1975 __isl_give isl_basic_set *isl_set_coefficients(
1976 __isl_take isl_set *set);
1977 __isl_give isl_union_set *isl_union_set_coefficients(
1978 __isl_take isl_union_set *bset);
1979 __isl_give isl_basic_set *isl_basic_set_solutions(
1980 __isl_take isl_basic_set *bset);
1981 __isl_give isl_basic_set *isl_set_solutions(
1982 __isl_take isl_set *set);
1983 __isl_give isl_union_set *isl_union_set_solutions(
1984 __isl_take isl_union_set *bset);
1988 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1990 __isl_give isl_union_map *isl_union_map_power(
1991 __isl_take isl_union_map *umap, int *exact);
1993 Compute a parametric representation for all positive powers I<k> of C<map>.
1994 The result maps I<k> to a nested relation corresponding to the
1995 I<k>th power of C<map>.
1996 The result may be an overapproximation. If the result is known to be exact,
1997 then C<*exact> is set to C<1>.
1999 =item * Transitive closure
2001 __isl_give isl_map *isl_map_transitive_closure(
2002 __isl_take isl_map *map, int *exact);
2003 __isl_give isl_union_map *isl_union_map_transitive_closure(
2004 __isl_take isl_union_map *umap, int *exact);
2006 Compute the transitive closure of C<map>.
2007 The result may be an overapproximation. If the result is known to be exact,
2008 then C<*exact> is set to C<1>.
2010 =item * Reaching path lengths
2012 __isl_give isl_map *isl_map_reaching_path_lengths(
2013 __isl_take isl_map *map, int *exact);
2015 Compute a relation that maps each element in the range of C<map>
2016 to the lengths of all paths composed of edges in C<map> that
2017 end up in the given element.
2018 The result may be an overapproximation. If the result is known to be exact,
2019 then C<*exact> is set to C<1>.
2020 To compute the I<maximal> path length, the resulting relation
2021 should be postprocessed by C<isl_map_lexmax>.
2022 In particular, if the input relation is a dependence relation
2023 (mapping sources to sinks), then the maximal path length corresponds
2024 to the free schedule.
2025 Note, however, that C<isl_map_lexmax> expects the maximum to be
2026 finite, so if the path lengths are unbounded (possibly due to
2027 the overapproximation), then you will get an error message.
2031 __isl_give isl_basic_set *isl_basic_map_wrap(
2032 __isl_take isl_basic_map *bmap);
2033 __isl_give isl_set *isl_map_wrap(
2034 __isl_take isl_map *map);
2035 __isl_give isl_union_set *isl_union_map_wrap(
2036 __isl_take isl_union_map *umap);
2037 __isl_give isl_basic_map *isl_basic_set_unwrap(
2038 __isl_take isl_basic_set *bset);
2039 __isl_give isl_map *isl_set_unwrap(
2040 __isl_take isl_set *set);
2041 __isl_give isl_union_map *isl_union_set_unwrap(
2042 __isl_take isl_union_set *uset);
2046 Remove any internal structure of domain (and range) of the given
2047 set or relation. If there is any such internal structure in the input,
2048 then the name of the space is also removed.
2050 __isl_give isl_basic_set *isl_basic_set_flatten(
2051 __isl_take isl_basic_set *bset);
2052 __isl_give isl_set *isl_set_flatten(
2053 __isl_take isl_set *set);
2054 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2055 __isl_take isl_basic_map *bmap);
2056 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2057 __isl_take isl_basic_map *bmap);
2058 __isl_give isl_map *isl_map_flatten_range(
2059 __isl_take isl_map *map);
2060 __isl_give isl_map *isl_map_flatten_domain(
2061 __isl_take isl_map *map);
2062 __isl_give isl_basic_map *isl_basic_map_flatten(
2063 __isl_take isl_basic_map *bmap);
2064 __isl_give isl_map *isl_map_flatten(
2065 __isl_take isl_map *map);
2067 __isl_give isl_map *isl_set_flatten_map(
2068 __isl_take isl_set *set);
2070 The function above constructs a relation
2071 that maps the input set to a flattened version of the set.
2075 Lift the input set to a space with extra dimensions corresponding
2076 to the existentially quantified variables in the input.
2077 In particular, the result lives in a wrapped map where the domain
2078 is the original space and the range corresponds to the original
2079 existentially quantified variables.
2081 __isl_give isl_basic_set *isl_basic_set_lift(
2082 __isl_take isl_basic_set *bset);
2083 __isl_give isl_set *isl_set_lift(
2084 __isl_take isl_set *set);
2085 __isl_give isl_union_set *isl_union_set_lift(
2086 __isl_take isl_union_set *uset);
2088 =item * Internal Product
2090 __isl_give isl_basic_map *isl_basic_map_zip(
2091 __isl_take isl_basic_map *bmap);
2092 __isl_give isl_map *isl_map_zip(
2093 __isl_take isl_map *map);
2094 __isl_give isl_union_map *isl_union_map_zip(
2095 __isl_take isl_union_map *umap);
2097 Given a relation with nested relations for domain and range,
2098 interchange the range of the domain with the domain of the range.
2100 =item * Aligning parameters
2102 __isl_give isl_set *isl_set_align_params(
2103 __isl_take isl_set *set,
2104 __isl_take isl_space *model);
2105 __isl_give isl_map *isl_map_align_params(
2106 __isl_take isl_map *map,
2107 __isl_take isl_space *model);
2109 Change the order of the parameters of the given set or relation
2110 such that the first parameters match those of C<model>.
2111 This may involve the introduction of extra parameters.
2112 All parameters need to be named.
2114 =item * Dimension manipulation
2116 __isl_give isl_set *isl_set_add_dims(
2117 __isl_take isl_set *set,
2118 enum isl_dim_type type, unsigned n);
2119 __isl_give isl_map *isl_map_add_dims(
2120 __isl_take isl_map *map,
2121 enum isl_dim_type type, unsigned n);
2122 __isl_give isl_set *isl_set_insert_dims(
2123 __isl_take isl_set *set,
2124 enum isl_dim_type type, unsigned pos, unsigned n);
2125 __isl_give isl_map *isl_map_insert_dims(
2126 __isl_take isl_map *map,
2127 enum isl_dim_type type, unsigned pos, unsigned n);
2128 __isl_give isl_basic_set *isl_basic_set_move_dims(
2129 __isl_take isl_basic_set *bset,
2130 enum isl_dim_type dst_type, unsigned dst_pos,
2131 enum isl_dim_type src_type, unsigned src_pos,
2133 __isl_give isl_basic_map *isl_basic_map_move_dims(
2134 __isl_take isl_basic_map *bmap,
2135 enum isl_dim_type dst_type, unsigned dst_pos,
2136 enum isl_dim_type src_type, unsigned src_pos,
2138 __isl_give isl_set *isl_set_move_dims(
2139 __isl_take isl_set *set,
2140 enum isl_dim_type dst_type, unsigned dst_pos,
2141 enum isl_dim_type src_type, unsigned src_pos,
2143 __isl_give isl_map *isl_map_move_dims(
2144 __isl_take isl_map *map,
2145 enum isl_dim_type dst_type, unsigned dst_pos,
2146 enum isl_dim_type src_type, unsigned src_pos,
2149 It is usually not advisable to directly change the (input or output)
2150 space of a set or a relation as this removes the name and the internal
2151 structure of the space. However, the above functions can be useful
2152 to add new parameters, assuming
2153 C<isl_set_align_params> and C<isl_map_align_params>
2158 =head2 Binary Operations
2160 The two arguments of a binary operation not only need to live
2161 in the same C<isl_ctx>, they currently also need to have
2162 the same (number of) parameters.
2164 =head3 Basic Operations
2168 =item * Intersection
2170 __isl_give isl_basic_set *isl_basic_set_intersect(
2171 __isl_take isl_basic_set *bset1,
2172 __isl_take isl_basic_set *bset2);
2173 __isl_give isl_set *isl_set_intersect_params(
2174 __isl_take isl_set *set,
2175 __isl_take isl_set *params);
2176 __isl_give isl_set *isl_set_intersect(
2177 __isl_take isl_set *set1,
2178 __isl_take isl_set *set2);
2179 __isl_give isl_union_set *isl_union_set_intersect(
2180 __isl_take isl_union_set *uset1,
2181 __isl_take isl_union_set *uset2);
2182 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2183 __isl_take isl_basic_map *bmap,
2184 __isl_take isl_basic_set *bset);
2185 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2186 __isl_take isl_basic_map *bmap,
2187 __isl_take isl_basic_set *bset);
2188 __isl_give isl_basic_map *isl_basic_map_intersect(
2189 __isl_take isl_basic_map *bmap1,
2190 __isl_take isl_basic_map *bmap2);
2191 __isl_give isl_map *isl_map_intersect_params(
2192 __isl_take isl_map *map,
2193 __isl_take isl_set *params);
2194 __isl_give isl_map *isl_map_intersect_domain(
2195 __isl_take isl_map *map,
2196 __isl_take isl_set *set);
2197 __isl_give isl_map *isl_map_intersect_range(
2198 __isl_take isl_map *map,
2199 __isl_take isl_set *set);
2200 __isl_give isl_map *isl_map_intersect(
2201 __isl_take isl_map *map1,
2202 __isl_take isl_map *map2);
2203 __isl_give isl_union_map *isl_union_map_intersect_domain(
2204 __isl_take isl_union_map *umap,
2205 __isl_take isl_union_set *uset);
2206 __isl_give isl_union_map *isl_union_map_intersect_range(
2207 __isl_take isl_union_map *umap,
2208 __isl_take isl_union_set *uset);
2209 __isl_give isl_union_map *isl_union_map_intersect(
2210 __isl_take isl_union_map *umap1,
2211 __isl_take isl_union_map *umap2);
2215 __isl_give isl_set *isl_basic_set_union(
2216 __isl_take isl_basic_set *bset1,
2217 __isl_take isl_basic_set *bset2);
2218 __isl_give isl_map *isl_basic_map_union(
2219 __isl_take isl_basic_map *bmap1,
2220 __isl_take isl_basic_map *bmap2);
2221 __isl_give isl_set *isl_set_union(
2222 __isl_take isl_set *set1,
2223 __isl_take isl_set *set2);
2224 __isl_give isl_map *isl_map_union(
2225 __isl_take isl_map *map1,
2226 __isl_take isl_map *map2);
2227 __isl_give isl_union_set *isl_union_set_union(
2228 __isl_take isl_union_set *uset1,
2229 __isl_take isl_union_set *uset2);
2230 __isl_give isl_union_map *isl_union_map_union(
2231 __isl_take isl_union_map *umap1,
2232 __isl_take isl_union_map *umap2);
2234 =item * Set difference
2236 __isl_give isl_set *isl_set_subtract(
2237 __isl_take isl_set *set1,
2238 __isl_take isl_set *set2);
2239 __isl_give isl_map *isl_map_subtract(
2240 __isl_take isl_map *map1,
2241 __isl_take isl_map *map2);
2242 __isl_give isl_union_set *isl_union_set_subtract(
2243 __isl_take isl_union_set *uset1,
2244 __isl_take isl_union_set *uset2);
2245 __isl_give isl_union_map *isl_union_map_subtract(
2246 __isl_take isl_union_map *umap1,
2247 __isl_take isl_union_map *umap2);
2251 __isl_give isl_basic_set *isl_basic_set_apply(
2252 __isl_take isl_basic_set *bset,
2253 __isl_take isl_basic_map *bmap);
2254 __isl_give isl_set *isl_set_apply(
2255 __isl_take isl_set *set,
2256 __isl_take isl_map *map);
2257 __isl_give isl_union_set *isl_union_set_apply(
2258 __isl_take isl_union_set *uset,
2259 __isl_take isl_union_map *umap);
2260 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2261 __isl_take isl_basic_map *bmap1,
2262 __isl_take isl_basic_map *bmap2);
2263 __isl_give isl_basic_map *isl_basic_map_apply_range(
2264 __isl_take isl_basic_map *bmap1,
2265 __isl_take isl_basic_map *bmap2);
2266 __isl_give isl_map *isl_map_apply_domain(
2267 __isl_take isl_map *map1,
2268 __isl_take isl_map *map2);
2269 __isl_give isl_union_map *isl_union_map_apply_domain(
2270 __isl_take isl_union_map *umap1,
2271 __isl_take isl_union_map *umap2);
2272 __isl_give isl_map *isl_map_apply_range(
2273 __isl_take isl_map *map1,
2274 __isl_take isl_map *map2);
2275 __isl_give isl_union_map *isl_union_map_apply_range(
2276 __isl_take isl_union_map *umap1,
2277 __isl_take isl_union_map *umap2);
2279 =item * Cartesian Product
2281 __isl_give isl_set *isl_set_product(
2282 __isl_take isl_set *set1,
2283 __isl_take isl_set *set2);
2284 __isl_give isl_union_set *isl_union_set_product(
2285 __isl_take isl_union_set *uset1,
2286 __isl_take isl_union_set *uset2);
2287 __isl_give isl_basic_map *isl_basic_map_domain_product(
2288 __isl_take isl_basic_map *bmap1,
2289 __isl_take isl_basic_map *bmap2);
2290 __isl_give isl_basic_map *isl_basic_map_range_product(
2291 __isl_take isl_basic_map *bmap1,
2292 __isl_take isl_basic_map *bmap2);
2293 __isl_give isl_map *isl_map_domain_product(
2294 __isl_take isl_map *map1,
2295 __isl_take isl_map *map2);
2296 __isl_give isl_map *isl_map_range_product(
2297 __isl_take isl_map *map1,
2298 __isl_take isl_map *map2);
2299 __isl_give isl_union_map *isl_union_map_range_product(
2300 __isl_take isl_union_map *umap1,
2301 __isl_take isl_union_map *umap2);
2302 __isl_give isl_map *isl_map_product(
2303 __isl_take isl_map *map1,
2304 __isl_take isl_map *map2);
2305 __isl_give isl_union_map *isl_union_map_product(
2306 __isl_take isl_union_map *umap1,
2307 __isl_take isl_union_map *umap2);
2309 The above functions compute the cross product of the given
2310 sets or relations. The domains and ranges of the results
2311 are wrapped maps between domains and ranges of the inputs.
2312 To obtain a ``flat'' product, use the following functions
2315 __isl_give isl_basic_set *isl_basic_set_flat_product(
2316 __isl_take isl_basic_set *bset1,
2317 __isl_take isl_basic_set *bset2);
2318 __isl_give isl_set *isl_set_flat_product(
2319 __isl_take isl_set *set1,
2320 __isl_take isl_set *set2);
2321 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2322 __isl_take isl_basic_map *bmap1,
2323 __isl_take isl_basic_map *bmap2);
2324 __isl_give isl_map *isl_map_flat_domain_product(
2325 __isl_take isl_map *map1,
2326 __isl_take isl_map *map2);
2327 __isl_give isl_map *isl_map_flat_range_product(
2328 __isl_take isl_map *map1,
2329 __isl_take isl_map *map2);
2330 __isl_give isl_union_map *isl_union_map_flat_range_product(
2331 __isl_take isl_union_map *umap1,
2332 __isl_take isl_union_map *umap2);
2333 __isl_give isl_basic_map *isl_basic_map_flat_product(
2334 __isl_take isl_basic_map *bmap1,
2335 __isl_take isl_basic_map *bmap2);
2336 __isl_give isl_map *isl_map_flat_product(
2337 __isl_take isl_map *map1,
2338 __isl_take isl_map *map2);
2340 =item * Simplification
2342 __isl_give isl_basic_set *isl_basic_set_gist(
2343 __isl_take isl_basic_set *bset,
2344 __isl_take isl_basic_set *context);
2345 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2346 __isl_take isl_set *context);
2347 __isl_give isl_set *isl_set_gist_params(
2348 __isl_take isl_set *set,
2349 __isl_take isl_set *context);
2350 __isl_give isl_union_set *isl_union_set_gist(
2351 __isl_take isl_union_set *uset,
2352 __isl_take isl_union_set *context);
2353 __isl_give isl_basic_map *isl_basic_map_gist(
2354 __isl_take isl_basic_map *bmap,
2355 __isl_take isl_basic_map *context);
2356 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2357 __isl_take isl_map *context);
2358 __isl_give isl_map *isl_map_gist_params(
2359 __isl_take isl_map *map,
2360 __isl_take isl_set *context);
2361 __isl_give isl_union_map *isl_union_map_gist(
2362 __isl_take isl_union_map *umap,
2363 __isl_take isl_union_map *context);
2365 The gist operation returns a set or relation that has the
2366 same intersection with the context as the input set or relation.
2367 Any implicit equality in the intersection is made explicit in the result,
2368 while all inequalities that are redundant with respect to the intersection
2370 In case of union sets and relations, the gist operation is performed
2375 =head3 Lexicographic Optimization
2377 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2378 the following functions
2379 compute a set that contains the lexicographic minimum or maximum
2380 of the elements in C<set> (or C<bset>) for those values of the parameters
2381 that satisfy C<dom>.
2382 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2383 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2385 In other words, the union of the parameter values
2386 for which the result is non-empty and of C<*empty>
2389 __isl_give isl_set *isl_basic_set_partial_lexmin(
2390 __isl_take isl_basic_set *bset,
2391 __isl_take isl_basic_set *dom,
2392 __isl_give isl_set **empty);
2393 __isl_give isl_set *isl_basic_set_partial_lexmax(
2394 __isl_take isl_basic_set *bset,
2395 __isl_take isl_basic_set *dom,
2396 __isl_give isl_set **empty);
2397 __isl_give isl_set *isl_set_partial_lexmin(
2398 __isl_take isl_set *set, __isl_take isl_set *dom,
2399 __isl_give isl_set **empty);
2400 __isl_give isl_set *isl_set_partial_lexmax(
2401 __isl_take isl_set *set, __isl_take isl_set *dom,
2402 __isl_give isl_set **empty);
2404 Given a (basic) set C<set> (or C<bset>), the following functions simply
2405 return a set containing the lexicographic minimum or maximum
2406 of the elements in C<set> (or C<bset>).
2407 In case of union sets, the optimum is computed per space.
2409 __isl_give isl_set *isl_basic_set_lexmin(
2410 __isl_take isl_basic_set *bset);
2411 __isl_give isl_set *isl_basic_set_lexmax(
2412 __isl_take isl_basic_set *bset);
2413 __isl_give isl_set *isl_set_lexmin(
2414 __isl_take isl_set *set);
2415 __isl_give isl_set *isl_set_lexmax(
2416 __isl_take isl_set *set);
2417 __isl_give isl_union_set *isl_union_set_lexmin(
2418 __isl_take isl_union_set *uset);
2419 __isl_give isl_union_set *isl_union_set_lexmax(
2420 __isl_take isl_union_set *uset);
2422 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2423 the following functions
2424 compute a relation that maps each element of C<dom>
2425 to the single lexicographic minimum or maximum
2426 of the elements that are associated to that same
2427 element in C<map> (or C<bmap>).
2428 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2429 that contains the elements in C<dom> that do not map
2430 to any elements in C<map> (or C<bmap>).
2431 In other words, the union of the domain of the result and of C<*empty>
2434 __isl_give isl_map *isl_basic_map_partial_lexmax(
2435 __isl_take isl_basic_map *bmap,
2436 __isl_take isl_basic_set *dom,
2437 __isl_give isl_set **empty);
2438 __isl_give isl_map *isl_basic_map_partial_lexmin(
2439 __isl_take isl_basic_map *bmap,
2440 __isl_take isl_basic_set *dom,
2441 __isl_give isl_set **empty);
2442 __isl_give isl_map *isl_map_partial_lexmax(
2443 __isl_take isl_map *map, __isl_take isl_set *dom,
2444 __isl_give isl_set **empty);
2445 __isl_give isl_map *isl_map_partial_lexmin(
2446 __isl_take isl_map *map, __isl_take isl_set *dom,
2447 __isl_give isl_set **empty);
2449 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2450 return a map mapping each element in the domain of
2451 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2452 of all elements associated to that element.
2453 In case of union relations, the optimum is computed per space.
2455 __isl_give isl_map *isl_basic_map_lexmin(
2456 __isl_take isl_basic_map *bmap);
2457 __isl_give isl_map *isl_basic_map_lexmax(
2458 __isl_take isl_basic_map *bmap);
2459 __isl_give isl_map *isl_map_lexmin(
2460 __isl_take isl_map *map);
2461 __isl_give isl_map *isl_map_lexmax(
2462 __isl_take isl_map *map);
2463 __isl_give isl_union_map *isl_union_map_lexmin(
2464 __isl_take isl_union_map *umap);
2465 __isl_give isl_union_map *isl_union_map_lexmax(
2466 __isl_take isl_union_map *umap);
2468 The following functions return their result in the form of
2469 a piecewise multi-affine expression
2470 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2471 but are otherwise equivalent to the corresponding functions
2472 returning a basic set or relation.
2474 __isl_give isl_pw_multi_aff *
2475 isl_basic_set_partial_lexmin_pw_multi_aff(
2476 __isl_take isl_basic_set *bset,
2477 __isl_take isl_basic_set *dom,
2478 __isl_give isl_set **empty);
2479 __isl_give isl_pw_multi_aff *
2480 isl_basic_set_partial_lexmax_pw_multi_aff(
2481 __isl_take isl_basic_set *bset,
2482 __isl_take isl_basic_set *dom,
2483 __isl_give isl_set **empty);
2484 __isl_give isl_pw_multi_aff *
2485 isl_basic_map_partial_lexmin_pw_multi_aff(
2486 __isl_take isl_basic_map *bmap,
2487 __isl_take isl_basic_set *dom,
2488 __isl_give isl_set **empty);
2489 __isl_give isl_pw_multi_aff *
2490 isl_basic_map_partial_lexmax_pw_multi_aff(
2491 __isl_take isl_basic_map *bmap,
2492 __isl_take isl_basic_set *dom,
2493 __isl_give isl_set **empty);
2497 Lists are defined over several element types, including
2498 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2499 Here we take lists of C<isl_set>s as an example.
2500 Lists can be created, copied and freed using the following functions.
2502 #include <isl/list.h>
2503 __isl_give isl_set_list *isl_set_list_from_set(
2504 __isl_take isl_set *el);
2505 __isl_give isl_set_list *isl_set_list_alloc(
2506 isl_ctx *ctx, int n);
2507 __isl_give isl_set_list *isl_set_list_copy(
2508 __isl_keep isl_set_list *list);
2509 __isl_give isl_set_list *isl_set_list_add(
2510 __isl_take isl_set_list *list,
2511 __isl_take isl_set *el);
2512 __isl_give isl_set_list *isl_set_list_concat(
2513 __isl_take isl_set_list *list1,
2514 __isl_take isl_set_list *list2);
2515 void *isl_set_list_free(__isl_take isl_set_list *list);
2517 C<isl_set_list_alloc> creates an empty list with a capacity for
2518 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2521 Lists can be inspected using the following functions.
2523 #include <isl/list.h>
2524 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2525 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2526 __isl_give isl_set *isl_set_list_get_set(
2527 __isl_keep isl_set_list *list, int index);
2528 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2529 int (*fn)(__isl_take isl_set *el, void *user),
2532 Lists can be printed using
2534 #include <isl/list.h>
2535 __isl_give isl_printer *isl_printer_print_set_list(
2536 __isl_take isl_printer *p,
2537 __isl_keep isl_set_list *list);
2541 Matrices can be created, copied and freed using the following functions.
2543 #include <isl/mat.h>
2544 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2545 unsigned n_row, unsigned n_col);
2546 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2547 void isl_mat_free(__isl_take isl_mat *mat);
2549 Note that the elements of a newly created matrix may have arbitrary values.
2550 The elements can be changed and inspected using the following functions.
2552 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2553 int isl_mat_rows(__isl_keep isl_mat *mat);
2554 int isl_mat_cols(__isl_keep isl_mat *mat);
2555 int isl_mat_get_element(__isl_keep isl_mat *mat,
2556 int row, int col, isl_int *v);
2557 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2558 int row, int col, isl_int v);
2559 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2560 int row, int col, int v);
2562 C<isl_mat_get_element> will return a negative value if anything went wrong.
2563 In that case, the value of C<*v> is undefined.
2565 The following function can be used to compute the (right) inverse
2566 of a matrix, i.e., a matrix such that the product of the original
2567 and the inverse (in that order) is a multiple of the identity matrix.
2568 The input matrix is assumed to be of full row-rank.
2570 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2572 The following function can be used to compute the (right) kernel
2573 (or null space) of a matrix, i.e., a matrix such that the product of
2574 the original and the kernel (in that order) is the zero matrix.
2576 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2578 =head2 Piecewise Quasi Affine Expressions
2580 The zero quasi affine expression on a given domain can be created using
2582 __isl_give isl_aff *isl_aff_zero_on_domain(
2583 __isl_take isl_local_space *ls);
2585 Note that the space in which the resulting object lives is a map space
2586 with the given space as domain and a one-dimensional range.
2588 An empty piecewise quasi affine expression (one with no cells)
2589 or a piecewise quasi affine expression with a single cell can
2590 be created using the following functions.
2592 #include <isl/aff.h>
2593 __isl_give isl_pw_aff *isl_pw_aff_empty(
2594 __isl_take isl_space *space);
2595 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2596 __isl_take isl_set *set, __isl_take isl_aff *aff);
2597 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2598 __isl_take isl_aff *aff);
2600 Quasi affine expressions can be copied and freed using
2602 #include <isl/aff.h>
2603 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2604 void *isl_aff_free(__isl_take isl_aff *aff);
2606 __isl_give isl_pw_aff *isl_pw_aff_copy(
2607 __isl_keep isl_pw_aff *pwaff);
2608 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2610 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2611 using the following function. The constraint is required to have
2612 a non-zero coefficient for the specified dimension.
2614 #include <isl/constraint.h>
2615 __isl_give isl_aff *isl_constraint_get_bound(
2616 __isl_keep isl_constraint *constraint,
2617 enum isl_dim_type type, int pos);
2619 The entire affine expression of the constraint can also be extracted
2620 using the following function.
2622 #include <isl/constraint.h>
2623 __isl_give isl_aff *isl_constraint_get_aff(
2624 __isl_keep isl_constraint *constraint);
2626 Conversely, an equality constraint equating
2627 the affine expression to zero or an inequality constraint enforcing
2628 the affine expression to be non-negative, can be constructed using
2630 __isl_give isl_constraint *isl_equality_from_aff(
2631 __isl_take isl_aff *aff);
2632 __isl_give isl_constraint *isl_inequality_from_aff(
2633 __isl_take isl_aff *aff);
2635 The expression can be inspected using
2637 #include <isl/aff.h>
2638 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2639 int isl_aff_dim(__isl_keep isl_aff *aff,
2640 enum isl_dim_type type);
2641 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2642 __isl_keep isl_aff *aff);
2643 __isl_give isl_local_space *isl_aff_get_local_space(
2644 __isl_keep isl_aff *aff);
2645 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2646 enum isl_dim_type type, unsigned pos);
2647 const char *isl_pw_aff_get_dim_name(
2648 __isl_keep isl_pw_aff *pa,
2649 enum isl_dim_type type, unsigned pos);
2650 __isl_give isl_id *isl_pw_aff_get_dim_id(
2651 __isl_keep isl_pw_aff *pa,
2652 enum isl_dim_type type, unsigned pos);
2653 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2655 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2656 enum isl_dim_type type, int pos, isl_int *v);
2657 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2659 __isl_give isl_aff *isl_aff_get_div(
2660 __isl_keep isl_aff *aff, int pos);
2662 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2663 int (*fn)(__isl_take isl_set *set,
2664 __isl_take isl_aff *aff,
2665 void *user), void *user);
2667 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2668 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2670 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2671 enum isl_dim_type type, unsigned first, unsigned n);
2672 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2673 enum isl_dim_type type, unsigned first, unsigned n);
2675 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2676 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2677 enum isl_dim_type type);
2678 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2680 It can be modified using
2682 #include <isl/aff.h>
2683 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2684 __isl_take isl_pw_aff *pwaff,
2685 enum isl_dim_type type, __isl_take isl_id *id);
2686 __isl_give isl_aff *isl_aff_set_dim_name(
2687 __isl_take isl_aff *aff, enum isl_dim_type type,
2688 unsigned pos, const char *s);
2689 __isl_give isl_aff *isl_aff_set_dim_id(
2690 __isl_take isl_aff *aff, enum isl_dim_type type,
2691 unsigned pos, __isl_take isl_id *id);
2692 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2693 __isl_take isl_pw_aff *pma,
2694 enum isl_dim_type type, unsigned pos,
2695 __isl_take isl_id *id);
2696 __isl_give isl_aff *isl_aff_set_constant(
2697 __isl_take isl_aff *aff, isl_int v);
2698 __isl_give isl_aff *isl_aff_set_constant_si(
2699 __isl_take isl_aff *aff, int v);
2700 __isl_give isl_aff *isl_aff_set_coefficient(
2701 __isl_take isl_aff *aff,
2702 enum isl_dim_type type, int pos, isl_int v);
2703 __isl_give isl_aff *isl_aff_set_coefficient_si(
2704 __isl_take isl_aff *aff,
2705 enum isl_dim_type type, int pos, int v);
2706 __isl_give isl_aff *isl_aff_set_denominator(
2707 __isl_take isl_aff *aff, isl_int v);
2709 __isl_give isl_aff *isl_aff_add_constant(
2710 __isl_take isl_aff *aff, isl_int v);
2711 __isl_give isl_aff *isl_aff_add_constant_si(
2712 __isl_take isl_aff *aff, int v);
2713 __isl_give isl_aff *isl_aff_add_coefficient(
2714 __isl_take isl_aff *aff,
2715 enum isl_dim_type type, int pos, isl_int v);
2716 __isl_give isl_aff *isl_aff_add_coefficient_si(
2717 __isl_take isl_aff *aff,
2718 enum isl_dim_type type, int pos, int v);
2720 __isl_give isl_aff *isl_aff_insert_dims(
2721 __isl_take isl_aff *aff,
2722 enum isl_dim_type type, unsigned first, unsigned n);
2723 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2724 __isl_take isl_pw_aff *pwaff,
2725 enum isl_dim_type type, unsigned first, unsigned n);
2726 __isl_give isl_aff *isl_aff_add_dims(
2727 __isl_take isl_aff *aff,
2728 enum isl_dim_type type, unsigned n);
2729 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2730 __isl_take isl_pw_aff *pwaff,
2731 enum isl_dim_type type, unsigned n);
2732 __isl_give isl_aff *isl_aff_drop_dims(
2733 __isl_take isl_aff *aff,
2734 enum isl_dim_type type, unsigned first, unsigned n);
2735 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2736 __isl_take isl_pw_aff *pwaff,
2737 enum isl_dim_type type, unsigned first, unsigned n);
2739 Note that the C<set_constant> and C<set_coefficient> functions
2740 set the I<numerator> of the constant or coefficient, while
2741 C<add_constant> and C<add_coefficient> add an integer value to
2742 the possibly rational constant or coefficient.
2744 To check whether an affine expressions is obviously zero
2745 or obviously equal to some other affine expression, use
2747 #include <isl/aff.h>
2748 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2749 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2750 __isl_keep isl_aff *aff2);
2751 int isl_pw_aff_plain_is_equal(
2752 __isl_keep isl_pw_aff *pwaff1,
2753 __isl_keep isl_pw_aff *pwaff2);
2757 #include <isl/aff.h>
2758 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2759 __isl_take isl_aff *aff2);
2760 __isl_give isl_pw_aff *isl_pw_aff_add(
2761 __isl_take isl_pw_aff *pwaff1,
2762 __isl_take isl_pw_aff *pwaff2);
2763 __isl_give isl_pw_aff *isl_pw_aff_min(
2764 __isl_take isl_pw_aff *pwaff1,
2765 __isl_take isl_pw_aff *pwaff2);
2766 __isl_give isl_pw_aff *isl_pw_aff_max(
2767 __isl_take isl_pw_aff *pwaff1,
2768 __isl_take isl_pw_aff *pwaff2);
2769 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2770 __isl_take isl_aff *aff2);
2771 __isl_give isl_pw_aff *isl_pw_aff_sub(
2772 __isl_take isl_pw_aff *pwaff1,
2773 __isl_take isl_pw_aff *pwaff2);
2774 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2775 __isl_give isl_pw_aff *isl_pw_aff_neg(
2776 __isl_take isl_pw_aff *pwaff);
2777 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2778 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2779 __isl_take isl_pw_aff *pwaff);
2780 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2781 __isl_give isl_pw_aff *isl_pw_aff_floor(
2782 __isl_take isl_pw_aff *pwaff);
2783 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2785 __isl_give isl_pw_aff *isl_pw_aff_mod(
2786 __isl_take isl_pw_aff *pwaff, isl_int mod);
2787 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2789 __isl_give isl_pw_aff *isl_pw_aff_scale(
2790 __isl_take isl_pw_aff *pwaff, isl_int f);
2791 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2793 __isl_give isl_aff *isl_aff_scale_down_ui(
2794 __isl_take isl_aff *aff, unsigned f);
2795 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2796 __isl_take isl_pw_aff *pwaff, isl_int f);
2798 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2799 __isl_take isl_pw_aff_list *list);
2800 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2801 __isl_take isl_pw_aff_list *list);
2803 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2804 __isl_take isl_pw_aff *pwqp);
2806 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2807 __isl_take isl_pw_aff *pwaff,
2808 __isl_take isl_space *model);
2810 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2811 __isl_take isl_set *context);
2812 __isl_give isl_pw_aff *isl_pw_aff_gist(
2813 __isl_take isl_pw_aff *pwaff,
2814 __isl_take isl_set *context);
2816 __isl_give isl_set *isl_pw_aff_domain(
2817 __isl_take isl_pw_aff *pwaff);
2818 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2819 __isl_take isl_pw_aff *pa,
2820 __isl_take isl_set *set);
2822 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2823 __isl_take isl_aff *aff2);
2824 __isl_give isl_pw_aff *isl_pw_aff_mul(
2825 __isl_take isl_pw_aff *pwaff1,
2826 __isl_take isl_pw_aff *pwaff2);
2828 When multiplying two affine expressions, at least one of the two needs
2831 #include <isl/aff.h>
2832 __isl_give isl_basic_set *isl_aff_le_basic_set(
2833 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2834 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2835 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2836 __isl_give isl_set *isl_pw_aff_eq_set(
2837 __isl_take isl_pw_aff *pwaff1,
2838 __isl_take isl_pw_aff *pwaff2);
2839 __isl_give isl_set *isl_pw_aff_ne_set(
2840 __isl_take isl_pw_aff *pwaff1,
2841 __isl_take isl_pw_aff *pwaff2);
2842 __isl_give isl_set *isl_pw_aff_le_set(
2843 __isl_take isl_pw_aff *pwaff1,
2844 __isl_take isl_pw_aff *pwaff2);
2845 __isl_give isl_set *isl_pw_aff_lt_set(
2846 __isl_take isl_pw_aff *pwaff1,
2847 __isl_take isl_pw_aff *pwaff2);
2848 __isl_give isl_set *isl_pw_aff_ge_set(
2849 __isl_take isl_pw_aff *pwaff1,
2850 __isl_take isl_pw_aff *pwaff2);
2851 __isl_give isl_set *isl_pw_aff_gt_set(
2852 __isl_take isl_pw_aff *pwaff1,
2853 __isl_take isl_pw_aff *pwaff2);
2855 __isl_give isl_set *isl_pw_aff_list_eq_set(
2856 __isl_take isl_pw_aff_list *list1,
2857 __isl_take isl_pw_aff_list *list2);
2858 __isl_give isl_set *isl_pw_aff_list_ne_set(
2859 __isl_take isl_pw_aff_list *list1,
2860 __isl_take isl_pw_aff_list *list2);
2861 __isl_give isl_set *isl_pw_aff_list_le_set(
2862 __isl_take isl_pw_aff_list *list1,
2863 __isl_take isl_pw_aff_list *list2);
2864 __isl_give isl_set *isl_pw_aff_list_lt_set(
2865 __isl_take isl_pw_aff_list *list1,
2866 __isl_take isl_pw_aff_list *list2);
2867 __isl_give isl_set *isl_pw_aff_list_ge_set(
2868 __isl_take isl_pw_aff_list *list1,
2869 __isl_take isl_pw_aff_list *list2);
2870 __isl_give isl_set *isl_pw_aff_list_gt_set(
2871 __isl_take isl_pw_aff_list *list1,
2872 __isl_take isl_pw_aff_list *list2);
2874 The function C<isl_aff_ge_basic_set> returns a basic set
2875 containing those elements in the shared space
2876 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2877 The function C<isl_aff_ge_set> returns a set
2878 containing those elements in the shared domain
2879 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2880 The functions operating on C<isl_pw_aff_list> apply the corresponding
2881 C<isl_pw_aff> function to each pair of elements in the two lists.
2883 #include <isl/aff.h>
2884 __isl_give isl_set *isl_pw_aff_nonneg_set(
2885 __isl_take isl_pw_aff *pwaff);
2886 __isl_give isl_set *isl_pw_aff_zero_set(
2887 __isl_take isl_pw_aff *pwaff);
2888 __isl_give isl_set *isl_pw_aff_non_zero_set(
2889 __isl_take isl_pw_aff *pwaff);
2891 The function C<isl_pw_aff_nonneg_set> returns a set
2892 containing those elements in the domain
2893 of C<pwaff> where C<pwaff> is non-negative.
2895 #include <isl/aff.h>
2896 __isl_give isl_pw_aff *isl_pw_aff_cond(
2897 __isl_take isl_set *cond,
2898 __isl_take isl_pw_aff *pwaff_true,
2899 __isl_take isl_pw_aff *pwaff_false);
2901 The function C<isl_pw_aff_cond> performs a conditional operator
2902 and returns an expression that is equal to C<pwaff_true>
2903 for elements in C<cond> and equal to C<pwaff_false> for elements
2906 #include <isl/aff.h>
2907 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2908 __isl_take isl_pw_aff *pwaff1,
2909 __isl_take isl_pw_aff *pwaff2);
2910 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2911 __isl_take isl_pw_aff *pwaff1,
2912 __isl_take isl_pw_aff *pwaff2);
2914 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2915 expression with a domain that is the union of those of C<pwaff1> and
2916 C<pwaff2> and such that on each cell, the quasi-affine expression is
2917 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2918 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2919 associated expression is the defined one.
2921 An expression can be printed using
2923 #include <isl/aff.h>
2924 __isl_give isl_printer *isl_printer_print_aff(
2925 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2927 __isl_give isl_printer *isl_printer_print_pw_aff(
2928 __isl_take isl_printer *p,
2929 __isl_keep isl_pw_aff *pwaff);
2931 =head2 Piecewise Multiple Quasi Affine Expressions
2933 An C<isl_multi_aff> object represents a sequence of
2934 zero or more affine expressions, all defined on the same domain space.
2936 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
2939 #include <isl/aff.h>
2940 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2941 __isl_take isl_space *space,
2942 __isl_take isl_aff_list *list);
2944 An empty piecewise multiple quasi affine expression (one with no cells) or
2945 a piecewise multiple quasi affine expression with a single cell can
2946 be created using the following functions.
2948 #include <isl/aff.h>
2949 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2950 __isl_take isl_space *space);
2951 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2952 __isl_take isl_set *set,
2953 __isl_take isl_multi_aff *maff);
2955 Multiple quasi affine expressions can be copied and freed using
2957 #include <isl/aff.h>
2958 __isl_give isl_multi_aff *isl_multi_aff_copy(
2959 __isl_keep isl_multi_aff *maff);
2960 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
2962 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2963 __isl_keep isl_pw_multi_aff *pma);
2964 void *isl_pw_multi_aff_free(
2965 __isl_take isl_pw_multi_aff *pma);
2967 The expression can be inspected using
2969 #include <isl/aff.h>
2970 isl_ctx *isl_multi_aff_get_ctx(
2971 __isl_keep isl_multi_aff *maff);
2972 isl_ctx *isl_pw_multi_aff_get_ctx(
2973 __isl_keep isl_pw_multi_aff *pma);
2974 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
2975 enum isl_dim_type type);
2976 unsigned isl_pw_multi_aff_dim(
2977 __isl_keep isl_pw_multi_aff *pma,
2978 enum isl_dim_type type);
2979 __isl_give isl_aff *isl_multi_aff_get_aff(
2980 __isl_keep isl_multi_aff *multi, int pos);
2981 const char *isl_pw_multi_aff_get_dim_name(
2982 __isl_keep isl_pw_multi_aff *pma,
2983 enum isl_dim_type type, unsigned pos);
2984 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
2985 __isl_keep isl_pw_multi_aff *pma,
2986 enum isl_dim_type type, unsigned pos);
2987 const char *isl_multi_aff_get_tuple_name(
2988 __isl_keep isl_multi_aff *multi,
2989 enum isl_dim_type type);
2990 const char *isl_pw_multi_aff_get_tuple_name(
2991 __isl_keep isl_pw_multi_aff *pma,
2992 enum isl_dim_type type);
2993 int isl_pw_multi_aff_has_tuple_id(
2994 __isl_keep isl_pw_multi_aff *pma,
2995 enum isl_dim_type type);
2996 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
2997 __isl_keep isl_pw_multi_aff *pma,
2998 enum isl_dim_type type);
3000 int isl_pw_multi_aff_foreach_piece(
3001 __isl_keep isl_pw_multi_aff *pma,
3002 int (*fn)(__isl_take isl_set *set,
3003 __isl_take isl_multi_aff *maff,
3004 void *user), void *user);
3006 It can be modified using
3008 #include <isl/aff.h>
3009 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3010 __isl_take isl_multi_aff *maff,
3011 enum isl_dim_type type, unsigned pos, const char *s);
3012 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3013 __isl_take isl_pw_multi_aff *pma,
3014 enum isl_dim_type type, __isl_take isl_id *id);
3016 To check whether two multiple affine expressions are
3017 obviously equal to each other, use
3019 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3020 __isl_keep isl_multi_aff *maff2);
3021 int isl_pw_multi_aff_plain_is_equal(
3022 __isl_keep isl_pw_multi_aff *pma1,
3023 __isl_keep isl_pw_multi_aff *pma2);
3027 #include <isl/aff.h>
3028 __isl_give isl_multi_aff *isl_multi_aff_add(
3029 __isl_take isl_multi_aff *maff1,
3030 __isl_take isl_multi_aff *maff2);
3031 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3032 __isl_take isl_pw_multi_aff *pma1,
3033 __isl_take isl_pw_multi_aff *pma2);
3034 __isl_give isl_multi_aff *isl_multi_aff_scale(
3035 __isl_take isl_multi_aff *maff,
3037 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3038 __isl_take isl_pw_multi_aff *pma,
3039 __isl_take isl_set *set);
3040 __isl_give isl_multi_aff *isl_multi_aff_gist(
3041 __isl_take isl_multi_aff *maff,
3042 __isl_take isl_set *context);
3044 An expression can be printed using
3046 #include <isl/aff.h>
3047 __isl_give isl_printer *isl_printer_print_multi_aff(
3048 __isl_take isl_printer *p,
3049 __isl_keep isl_multi_aff *maff);
3050 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3051 __isl_take isl_printer *p,
3052 __isl_keep isl_pw_multi_aff *pma);
3056 Points are elements of a set. They can be used to construct
3057 simple sets (boxes) or they can be used to represent the
3058 individual elements of a set.
3059 The zero point (the origin) can be created using
3061 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3063 The coordinates of a point can be inspected, set and changed
3066 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
3067 enum isl_dim_type type, int pos, isl_int *v);
3068 __isl_give isl_point *isl_point_set_coordinate(
3069 __isl_take isl_point *pnt,
3070 enum isl_dim_type type, int pos, isl_int v);
3072 __isl_give isl_point *isl_point_add_ui(
3073 __isl_take isl_point *pnt,
3074 enum isl_dim_type type, int pos, unsigned val);
3075 __isl_give isl_point *isl_point_sub_ui(
3076 __isl_take isl_point *pnt,
3077 enum isl_dim_type type, int pos, unsigned val);
3079 Other properties can be obtained using
3081 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3083 Points can be copied or freed using
3085 __isl_give isl_point *isl_point_copy(
3086 __isl_keep isl_point *pnt);
3087 void isl_point_free(__isl_take isl_point *pnt);
3089 A singleton set can be created from a point using
3091 __isl_give isl_basic_set *isl_basic_set_from_point(
3092 __isl_take isl_point *pnt);
3093 __isl_give isl_set *isl_set_from_point(
3094 __isl_take isl_point *pnt);
3096 and a box can be created from two opposite extremal points using
3098 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3099 __isl_take isl_point *pnt1,
3100 __isl_take isl_point *pnt2);
3101 __isl_give isl_set *isl_set_box_from_points(
3102 __isl_take isl_point *pnt1,
3103 __isl_take isl_point *pnt2);
3105 All elements of a B<bounded> (union) set can be enumerated using
3106 the following functions.
3108 int isl_set_foreach_point(__isl_keep isl_set *set,
3109 int (*fn)(__isl_take isl_point *pnt, void *user),
3111 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3112 int (*fn)(__isl_take isl_point *pnt, void *user),
3115 The function C<fn> is called for each integer point in
3116 C<set> with as second argument the last argument of
3117 the C<isl_set_foreach_point> call. The function C<fn>
3118 should return C<0> on success and C<-1> on failure.
3119 In the latter case, C<isl_set_foreach_point> will stop
3120 enumerating and return C<-1> as well.
3121 If the enumeration is performed successfully and to completion,
3122 then C<isl_set_foreach_point> returns C<0>.
3124 To obtain a single point of a (basic) set, use
3126 __isl_give isl_point *isl_basic_set_sample_point(
3127 __isl_take isl_basic_set *bset);
3128 __isl_give isl_point *isl_set_sample_point(
3129 __isl_take isl_set *set);
3131 If C<set> does not contain any (integer) points, then the
3132 resulting point will be ``void'', a property that can be
3135 int isl_point_is_void(__isl_keep isl_point *pnt);
3137 =head2 Piecewise Quasipolynomials
3139 A piecewise quasipolynomial is a particular kind of function that maps
3140 a parametric point to a rational value.
3141 More specifically, a quasipolynomial is a polynomial expression in greatest
3142 integer parts of affine expressions of parameters and variables.
3143 A piecewise quasipolynomial is a subdivision of a given parametric
3144 domain into disjoint cells with a quasipolynomial associated to
3145 each cell. The value of the piecewise quasipolynomial at a given
3146 point is the value of the quasipolynomial associated to the cell
3147 that contains the point. Outside of the union of cells,
3148 the value is assumed to be zero.
3149 For example, the piecewise quasipolynomial
3151 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3153 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3154 A given piecewise quasipolynomial has a fixed domain dimension.
3155 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3156 defined over different domains.
3157 Piecewise quasipolynomials are mainly used by the C<barvinok>
3158 library for representing the number of elements in a parametric set or map.
3159 For example, the piecewise quasipolynomial above represents
3160 the number of points in the map
3162 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3164 =head3 Printing (Piecewise) Quasipolynomials
3166 Quasipolynomials and piecewise quasipolynomials can be printed
3167 using the following functions.
3169 __isl_give isl_printer *isl_printer_print_qpolynomial(
3170 __isl_take isl_printer *p,
3171 __isl_keep isl_qpolynomial *qp);
3173 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3174 __isl_take isl_printer *p,
3175 __isl_keep isl_pw_qpolynomial *pwqp);
3177 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3178 __isl_take isl_printer *p,
3179 __isl_keep isl_union_pw_qpolynomial *upwqp);
3181 The output format of the printer
3182 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3183 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3185 In case of printing in C<ISL_FORMAT_C>, the user may want
3186 to set the names of all dimensions
3188 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3189 __isl_take isl_qpolynomial *qp,
3190 enum isl_dim_type type, unsigned pos,
3192 __isl_give isl_pw_qpolynomial *
3193 isl_pw_qpolynomial_set_dim_name(
3194 __isl_take isl_pw_qpolynomial *pwqp,
3195 enum isl_dim_type type, unsigned pos,
3198 =head3 Creating New (Piecewise) Quasipolynomials
3200 Some simple quasipolynomials can be created using the following functions.
3201 More complicated quasipolynomials can be created by applying
3202 operations such as addition and multiplication
3203 on the resulting quasipolynomials
3205 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3206 __isl_take isl_space *domain);
3207 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3208 __isl_take isl_space *domain);
3209 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3210 __isl_take isl_space *domain);
3211 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3212 __isl_take isl_space *domain);
3213 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3214 __isl_take isl_space *domain);
3215 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3216 __isl_take isl_space *domain,
3217 const isl_int n, const isl_int d);
3218 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3219 __isl_take isl_space *domain,
3220 enum isl_dim_type type, unsigned pos);
3221 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3222 __isl_take isl_aff *aff);
3224 Note that the space in which a quasipolynomial lives is a map space
3225 with a one-dimensional range. The C<domain> argument in some of
3226 the functions above corresponds to the domain of this map space.
3228 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3229 with a single cell can be created using the following functions.
3230 Multiple of these single cell piecewise quasipolynomials can
3231 be combined to create more complicated piecewise quasipolynomials.
3233 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3234 __isl_take isl_space *space);
3235 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3236 __isl_take isl_set *set,
3237 __isl_take isl_qpolynomial *qp);
3238 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3239 __isl_take isl_qpolynomial *qp);
3240 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3241 __isl_take isl_pw_aff *pwaff);
3243 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3244 __isl_take isl_space *space);
3245 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3246 __isl_take isl_pw_qpolynomial *pwqp);
3247 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3248 __isl_take isl_union_pw_qpolynomial *upwqp,
3249 __isl_take isl_pw_qpolynomial *pwqp);
3251 Quasipolynomials can be copied and freed again using the following
3254 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3255 __isl_keep isl_qpolynomial *qp);
3256 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3258 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3259 __isl_keep isl_pw_qpolynomial *pwqp);
3260 void *isl_pw_qpolynomial_free(
3261 __isl_take isl_pw_qpolynomial *pwqp);
3263 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3264 __isl_keep isl_union_pw_qpolynomial *upwqp);
3265 void isl_union_pw_qpolynomial_free(
3266 __isl_take isl_union_pw_qpolynomial *upwqp);
3268 =head3 Inspecting (Piecewise) Quasipolynomials
3270 To iterate over all piecewise quasipolynomials in a union
3271 piecewise quasipolynomial, use the following function
3273 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3274 __isl_keep isl_union_pw_qpolynomial *upwqp,
3275 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3278 To extract the piecewise quasipolynomial in a given space from a union, use
3280 __isl_give isl_pw_qpolynomial *
3281 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3282 __isl_keep isl_union_pw_qpolynomial *upwqp,
3283 __isl_take isl_space *space);
3285 To iterate over the cells in a piecewise quasipolynomial,
3286 use either of the following two functions
3288 int isl_pw_qpolynomial_foreach_piece(
3289 __isl_keep isl_pw_qpolynomial *pwqp,
3290 int (*fn)(__isl_take isl_set *set,
3291 __isl_take isl_qpolynomial *qp,
3292 void *user), void *user);
3293 int isl_pw_qpolynomial_foreach_lifted_piece(
3294 __isl_keep isl_pw_qpolynomial *pwqp,
3295 int (*fn)(__isl_take isl_set *set,
3296 __isl_take isl_qpolynomial *qp,
3297 void *user), void *user);
3299 As usual, the function C<fn> should return C<0> on success
3300 and C<-1> on failure. The difference between
3301 C<isl_pw_qpolynomial_foreach_piece> and
3302 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3303 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3304 compute unique representations for all existentially quantified
3305 variables and then turn these existentially quantified variables
3306 into extra set variables, adapting the associated quasipolynomial
3307 accordingly. This means that the C<set> passed to C<fn>
3308 will not have any existentially quantified variables, but that
3309 the dimensions of the sets may be different for different
3310 invocations of C<fn>.
3312 To iterate over all terms in a quasipolynomial,
3315 int isl_qpolynomial_foreach_term(
3316 __isl_keep isl_qpolynomial *qp,
3317 int (*fn)(__isl_take isl_term *term,
3318 void *user), void *user);
3320 The terms themselves can be inspected and freed using
3323 unsigned isl_term_dim(__isl_keep isl_term *term,
3324 enum isl_dim_type type);
3325 void isl_term_get_num(__isl_keep isl_term *term,
3327 void isl_term_get_den(__isl_keep isl_term *term,
3329 int isl_term_get_exp(__isl_keep isl_term *term,
3330 enum isl_dim_type type, unsigned pos);
3331 __isl_give isl_aff *isl_term_get_div(
3332 __isl_keep isl_term *term, unsigned pos);
3333 void isl_term_free(__isl_take isl_term *term);
3335 Each term is a product of parameters, set variables and
3336 integer divisions. The function C<isl_term_get_exp>
3337 returns the exponent of a given dimensions in the given term.
3338 The C<isl_int>s in the arguments of C<isl_term_get_num>
3339 and C<isl_term_get_den> need to have been initialized
3340 using C<isl_int_init> before calling these functions.
3342 =head3 Properties of (Piecewise) Quasipolynomials
3344 To check whether a quasipolynomial is actually a constant,
3345 use the following function.
3347 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3348 isl_int *n, isl_int *d);
3350 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3351 then the numerator and denominator of the constant
3352 are returned in C<*n> and C<*d>, respectively.
3354 To check whether two union piecewise quasipolynomials are
3355 obviously equal, use
3357 int isl_union_pw_qpolynomial_plain_is_equal(
3358 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3359 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3361 =head3 Operations on (Piecewise) Quasipolynomials
3363 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3364 __isl_take isl_qpolynomial *qp, isl_int v);
3365 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3366 __isl_take isl_qpolynomial *qp);
3367 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3368 __isl_take isl_qpolynomial *qp1,
3369 __isl_take isl_qpolynomial *qp2);
3370 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3371 __isl_take isl_qpolynomial *qp1,
3372 __isl_take isl_qpolynomial *qp2);
3373 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3374 __isl_take isl_qpolynomial *qp1,
3375 __isl_take isl_qpolynomial *qp2);
3376 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3377 __isl_take isl_qpolynomial *qp, unsigned exponent);
3379 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3380 __isl_take isl_pw_qpolynomial *pwqp1,
3381 __isl_take isl_pw_qpolynomial *pwqp2);
3382 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3383 __isl_take isl_pw_qpolynomial *pwqp1,
3384 __isl_take isl_pw_qpolynomial *pwqp2);
3385 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3386 __isl_take isl_pw_qpolynomial *pwqp1,
3387 __isl_take isl_pw_qpolynomial *pwqp2);
3388 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3389 __isl_take isl_pw_qpolynomial *pwqp);
3390 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3391 __isl_take isl_pw_qpolynomial *pwqp1,
3392 __isl_take isl_pw_qpolynomial *pwqp2);
3393 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3394 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3396 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3397 __isl_take isl_union_pw_qpolynomial *upwqp1,
3398 __isl_take isl_union_pw_qpolynomial *upwqp2);
3399 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3400 __isl_take isl_union_pw_qpolynomial *upwqp1,
3401 __isl_take isl_union_pw_qpolynomial *upwqp2);
3402 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3403 __isl_take isl_union_pw_qpolynomial *upwqp1,
3404 __isl_take isl_union_pw_qpolynomial *upwqp2);
3406 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3407 __isl_take isl_pw_qpolynomial *pwqp,
3408 __isl_take isl_point *pnt);
3410 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3411 __isl_take isl_union_pw_qpolynomial *upwqp,
3412 __isl_take isl_point *pnt);
3414 __isl_give isl_set *isl_pw_qpolynomial_domain(
3415 __isl_take isl_pw_qpolynomial *pwqp);
3416 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3417 __isl_take isl_pw_qpolynomial *pwpq,
3418 __isl_take isl_set *set);
3420 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3421 __isl_take isl_union_pw_qpolynomial *upwqp);
3422 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3423 __isl_take isl_union_pw_qpolynomial *upwpq,
3424 __isl_take isl_union_set *uset);
3426 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3427 __isl_take isl_qpolynomial *qp,
3428 __isl_take isl_space *model);
3430 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3431 __isl_take isl_qpolynomial *qp);
3432 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3433 __isl_take isl_pw_qpolynomial *pwqp);
3435 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3436 __isl_take isl_union_pw_qpolynomial *upwqp);
3438 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3439 __isl_take isl_qpolynomial *qp,
3440 __isl_take isl_set *context);
3442 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3443 __isl_take isl_pw_qpolynomial *pwqp,
3444 __isl_take isl_set *context);
3446 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3447 __isl_take isl_union_pw_qpolynomial *upwqp,
3448 __isl_take isl_union_set *context);
3450 The gist operation applies the gist operation to each of
3451 the cells in the domain of the input piecewise quasipolynomial.
3452 The context is also exploited
3453 to simplify the quasipolynomials associated to each cell.
3455 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3456 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3457 __isl_give isl_union_pw_qpolynomial *
3458 isl_union_pw_qpolynomial_to_polynomial(
3459 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3461 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3462 the polynomial will be an overapproximation. If C<sign> is negative,
3463 it will be an underapproximation. If C<sign> is zero, the approximation
3464 will lie somewhere in between.
3466 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3468 A piecewise quasipolynomial reduction is a piecewise
3469 reduction (or fold) of quasipolynomials.
3470 In particular, the reduction can be maximum or a minimum.
3471 The objects are mainly used to represent the result of
3472 an upper or lower bound on a quasipolynomial over its domain,
3473 i.e., as the result of the following function.
3475 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3476 __isl_take isl_pw_qpolynomial *pwqp,
3477 enum isl_fold type, int *tight);
3479 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3480 __isl_take isl_union_pw_qpolynomial *upwqp,
3481 enum isl_fold type, int *tight);
3483 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3484 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3485 is the returned bound is known be tight, i.e., for each value
3486 of the parameters there is at least
3487 one element in the domain that reaches the bound.
3488 If the domain of C<pwqp> is not wrapping, then the bound is computed
3489 over all elements in that domain and the result has a purely parametric
3490 domain. If the domain of C<pwqp> is wrapping, then the bound is
3491 computed over the range of the wrapped relation. The domain of the
3492 wrapped relation becomes the domain of the result.
3494 A (piecewise) quasipolynomial reduction can be copied or freed using the
3495 following functions.
3497 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3498 __isl_keep isl_qpolynomial_fold *fold);
3499 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3500 __isl_keep isl_pw_qpolynomial_fold *pwf);
3501 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3502 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3503 void isl_qpolynomial_fold_free(
3504 __isl_take isl_qpolynomial_fold *fold);
3505 void *isl_pw_qpolynomial_fold_free(
3506 __isl_take isl_pw_qpolynomial_fold *pwf);
3507 void isl_union_pw_qpolynomial_fold_free(
3508 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3510 =head3 Printing Piecewise Quasipolynomial Reductions
3512 Piecewise quasipolynomial reductions can be printed
3513 using the following function.
3515 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3516 __isl_take isl_printer *p,
3517 __isl_keep isl_pw_qpolynomial_fold *pwf);
3518 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3519 __isl_take isl_printer *p,
3520 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3522 For C<isl_printer_print_pw_qpolynomial_fold>,
3523 output format of the printer
3524 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3525 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3526 output format of the printer
3527 needs to be set to C<ISL_FORMAT_ISL>.
3528 In case of printing in C<ISL_FORMAT_C>, the user may want
3529 to set the names of all dimensions
3531 __isl_give isl_pw_qpolynomial_fold *
3532 isl_pw_qpolynomial_fold_set_dim_name(
3533 __isl_take isl_pw_qpolynomial_fold *pwf,
3534 enum isl_dim_type type, unsigned pos,
3537 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3539 To iterate over all piecewise quasipolynomial reductions in a union
3540 piecewise quasipolynomial reduction, use the following function
3542 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3543 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3544 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3545 void *user), void *user);
3547 To iterate over the cells in a piecewise quasipolynomial reduction,
3548 use either of the following two functions
3550 int isl_pw_qpolynomial_fold_foreach_piece(
3551 __isl_keep isl_pw_qpolynomial_fold *pwf,
3552 int (*fn)(__isl_take isl_set *set,
3553 __isl_take isl_qpolynomial_fold *fold,
3554 void *user), void *user);
3555 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3556 __isl_keep isl_pw_qpolynomial_fold *pwf,
3557 int (*fn)(__isl_take isl_set *set,
3558 __isl_take isl_qpolynomial_fold *fold,
3559 void *user), void *user);
3561 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3562 of the difference between these two functions.
3564 To iterate over all quasipolynomials in a reduction, use
3566 int isl_qpolynomial_fold_foreach_qpolynomial(
3567 __isl_keep isl_qpolynomial_fold *fold,
3568 int (*fn)(__isl_take isl_qpolynomial *qp,
3569 void *user), void *user);
3571 =head3 Properties of Piecewise Quasipolynomial Reductions
3573 To check whether two union piecewise quasipolynomial reductions are
3574 obviously equal, use
3576 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3577 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3578 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3580 =head3 Operations on Piecewise Quasipolynomial Reductions
3582 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3583 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3585 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3586 __isl_take isl_pw_qpolynomial_fold *pwf1,
3587 __isl_take isl_pw_qpolynomial_fold *pwf2);
3589 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3590 __isl_take isl_pw_qpolynomial_fold *pwf1,
3591 __isl_take isl_pw_qpolynomial_fold *pwf2);
3593 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3594 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3595 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3597 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3598 __isl_take isl_pw_qpolynomial_fold *pwf,
3599 __isl_take isl_point *pnt);
3601 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3602 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3603 __isl_take isl_point *pnt);
3605 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3606 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3607 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3608 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3609 __isl_take isl_union_set *uset);
3611 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3612 __isl_take isl_pw_qpolynomial_fold *pwf);
3614 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3615 __isl_take isl_pw_qpolynomial_fold *pwf);
3617 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3618 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3620 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3621 __isl_take isl_pw_qpolynomial_fold *pwf,
3622 __isl_take isl_set *context);
3624 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3625 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3626 __isl_take isl_union_set *context);
3628 The gist operation applies the gist operation to each of
3629 the cells in the domain of the input piecewise quasipolynomial reduction.
3630 In future, the operation will also exploit the context
3631 to simplify the quasipolynomial reductions associated to each cell.
3633 __isl_give isl_pw_qpolynomial_fold *
3634 isl_set_apply_pw_qpolynomial_fold(
3635 __isl_take isl_set *set,
3636 __isl_take isl_pw_qpolynomial_fold *pwf,
3638 __isl_give isl_pw_qpolynomial_fold *
3639 isl_map_apply_pw_qpolynomial_fold(
3640 __isl_take isl_map *map,
3641 __isl_take isl_pw_qpolynomial_fold *pwf,
3643 __isl_give isl_union_pw_qpolynomial_fold *
3644 isl_union_set_apply_union_pw_qpolynomial_fold(
3645 __isl_take isl_union_set *uset,
3646 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3648 __isl_give isl_union_pw_qpolynomial_fold *
3649 isl_union_map_apply_union_pw_qpolynomial_fold(
3650 __isl_take isl_union_map *umap,
3651 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3654 The functions taking a map
3655 compose the given map with the given piecewise quasipolynomial reduction.
3656 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3657 over all elements in the intersection of the range of the map
3658 and the domain of the piecewise quasipolynomial reduction
3659 as a function of an element in the domain of the map.
3660 The functions taking a set compute a bound over all elements in the
3661 intersection of the set and the domain of the
3662 piecewise quasipolynomial reduction.
3664 =head2 Dependence Analysis
3666 C<isl> contains specialized functionality for performing
3667 array dataflow analysis. That is, given a I<sink> access relation
3668 and a collection of possible I<source> access relations,
3669 C<isl> can compute relations that describe
3670 for each iteration of the sink access, which iteration
3671 of which of the source access relations was the last
3672 to access the same data element before the given iteration
3674 To compute standard flow dependences, the sink should be
3675 a read, while the sources should be writes.
3676 If any of the source accesses are marked as being I<may>
3677 accesses, then there will be a dependence to the last
3678 I<must> access B<and> to any I<may> access that follows
3679 this last I<must> access.
3680 In particular, if I<all> sources are I<may> accesses,
3681 then memory based dependence analysis is performed.
3682 If, on the other hand, all sources are I<must> accesses,
3683 then value based dependence analysis is performed.
3685 #include <isl/flow.h>
3687 typedef int (*isl_access_level_before)(void *first, void *second);
3689 __isl_give isl_access_info *isl_access_info_alloc(
3690 __isl_take isl_map *sink,
3691 void *sink_user, isl_access_level_before fn,
3693 __isl_give isl_access_info *isl_access_info_add_source(
3694 __isl_take isl_access_info *acc,
3695 __isl_take isl_map *source, int must,
3697 void isl_access_info_free(__isl_take isl_access_info *acc);
3699 __isl_give isl_flow *isl_access_info_compute_flow(
3700 __isl_take isl_access_info *acc);
3702 int isl_flow_foreach(__isl_keep isl_flow *deps,
3703 int (*fn)(__isl_take isl_map *dep, int must,
3704 void *dep_user, void *user),
3706 __isl_give isl_map *isl_flow_get_no_source(
3707 __isl_keep isl_flow *deps, int must);
3708 void isl_flow_free(__isl_take isl_flow *deps);
3710 The function C<isl_access_info_compute_flow> performs the actual
3711 dependence analysis. The other functions are used to construct
3712 the input for this function or to read off the output.
3714 The input is collected in an C<isl_access_info>, which can
3715 be created through a call to C<isl_access_info_alloc>.
3716 The arguments to this functions are the sink access relation
3717 C<sink>, a token C<sink_user> used to identify the sink
3718 access to the user, a callback function for specifying the
3719 relative order of source and sink accesses, and the number
3720 of source access relations that will be added.
3721 The callback function has type C<int (*)(void *first, void *second)>.
3722 The function is called with two user supplied tokens identifying
3723 either a source or the sink and it should return the shared nesting
3724 level and the relative order of the two accesses.
3725 In particular, let I<n> be the number of loops shared by
3726 the two accesses. If C<first> precedes C<second> textually,
3727 then the function should return I<2 * n + 1>; otherwise,
3728 it should return I<2 * n>.
3729 The sources can be added to the C<isl_access_info> by performing
3730 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3731 C<must> indicates whether the source is a I<must> access
3732 or a I<may> access. Note that a multi-valued access relation
3733 should only be marked I<must> if every iteration in the domain
3734 of the relation accesses I<all> elements in its image.
3735 The C<source_user> token is again used to identify
3736 the source access. The range of the source access relation
3737 C<source> should have the same dimension as the range
3738 of the sink access relation.
3739 The C<isl_access_info_free> function should usually not be
3740 called explicitly, because it is called implicitly by
3741 C<isl_access_info_compute_flow>.
3743 The result of the dependence analysis is collected in an
3744 C<isl_flow>. There may be elements of
3745 the sink access for which no preceding source access could be
3746 found or for which all preceding sources are I<may> accesses.
3747 The relations containing these elements can be obtained through
3748 calls to C<isl_flow_get_no_source>, the first with C<must> set
3749 and the second with C<must> unset.
3750 In the case of standard flow dependence analysis,
3751 with the sink a read and the sources I<must> writes,
3752 the first relation corresponds to the reads from uninitialized
3753 array elements and the second relation is empty.
3754 The actual flow dependences can be extracted using
3755 C<isl_flow_foreach>. This function will call the user-specified
3756 callback function C<fn> for each B<non-empty> dependence between
3757 a source and the sink. The callback function is called
3758 with four arguments, the actual flow dependence relation
3759 mapping source iterations to sink iterations, a boolean that
3760 indicates whether it is a I<must> or I<may> dependence, a token
3761 identifying the source and an additional C<void *> with value
3762 equal to the third argument of the C<isl_flow_foreach> call.
3763 A dependence is marked I<must> if it originates from a I<must>
3764 source and if it is not followed by any I<may> sources.
3766 After finishing with an C<isl_flow>, the user should call
3767 C<isl_flow_free> to free all associated memory.
3769 A higher-level interface to dependence analysis is provided
3770 by the following function.
3772 #include <isl/flow.h>
3774 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3775 __isl_take isl_union_map *must_source,
3776 __isl_take isl_union_map *may_source,
3777 __isl_take isl_union_map *schedule,
3778 __isl_give isl_union_map **must_dep,
3779 __isl_give isl_union_map **may_dep,
3780 __isl_give isl_union_map **must_no_source,
3781 __isl_give isl_union_map **may_no_source);
3783 The arrays are identified by the tuple names of the ranges
3784 of the accesses. The iteration domains by the tuple names
3785 of the domains of the accesses and of the schedule.
3786 The relative order of the iteration domains is given by the
3787 schedule. The relations returned through C<must_no_source>
3788 and C<may_no_source> are subsets of C<sink>.
3789 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3790 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3791 any of the other arguments is treated as an error.
3795 B<The functionality described in this section is fairly new
3796 and may be subject to change.>
3798 The following function can be used to compute a schedule
3799 for a union of domains. The generated schedule respects
3800 all C<validity> dependences. That is, all dependence distances
3801 over these dependences in the scheduled space are lexicographically
3802 positive. The generated schedule schedule also tries to minimize
3803 the dependence distances over C<proximity> dependences.
3804 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3805 for groups of domains where the dependence distances have only
3806 non-negative values.
3807 The algorithm used to construct the schedule is similar to that
3810 #include <isl/schedule.h>
3811 __isl_give isl_schedule *isl_union_set_compute_schedule(
3812 __isl_take isl_union_set *domain,
3813 __isl_take isl_union_map *validity,
3814 __isl_take isl_union_map *proximity);
3815 void *isl_schedule_free(__isl_take isl_schedule *sched);
3817 A mapping from the domains to the scheduled space can be obtained
3818 from an C<isl_schedule> using the following function.
3820 __isl_give isl_union_map *isl_schedule_get_map(
3821 __isl_keep isl_schedule *sched);
3823 A representation of the schedule can be printed using
3825 __isl_give isl_printer *isl_printer_print_schedule(
3826 __isl_take isl_printer *p,
3827 __isl_keep isl_schedule *schedule);
3829 A representation of the schedule as a forest of bands can be obtained
3830 using the following function.
3832 __isl_give isl_band_list *isl_schedule_get_band_forest(
3833 __isl_keep isl_schedule *schedule);
3835 The list can be manipulated as explained in L<"Lists">.
3836 The bands inside the list can be copied and freed using the following
3839 #include <isl/band.h>
3840 __isl_give isl_band *isl_band_copy(
3841 __isl_keep isl_band *band);
3842 void *isl_band_free(__isl_take isl_band *band);
3844 Each band contains zero or more scheduling dimensions.
3845 These are referred to as the members of the band.
3846 The section of the schedule that corresponds to the band is
3847 referred to as the partial schedule of the band.
3848 For those nodes that participate in a band, the outer scheduling
3849 dimensions form the prefix schedule, while the inner scheduling
3850 dimensions form the suffix schedule.
3851 That is, if we take a cut of the band forest, then the union of
3852 the concatenations of the prefix, partial and suffix schedules of
3853 each band in the cut is equal to the entire schedule (modulo
3854 some possible padding at the end with zero scheduling dimensions).
3855 The properties of a band can be inspected using the following functions.
3857 #include <isl/band.h>
3858 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3860 int isl_band_has_children(__isl_keep isl_band *band);
3861 __isl_give isl_band_list *isl_band_get_children(
3862 __isl_keep isl_band *band);
3864 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3865 __isl_keep isl_band *band);
3866 __isl_give isl_union_map *isl_band_get_partial_schedule(
3867 __isl_keep isl_band *band);
3868 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3869 __isl_keep isl_band *band);
3871 int isl_band_n_member(__isl_keep isl_band *band);
3872 int isl_band_member_is_zero_distance(
3873 __isl_keep isl_band *band, int pos);
3875 Note that a scheduling dimension is considered to be ``zero
3876 distance'' if it does not carry any proximity dependences
3878 That is, if the dependence distances of the proximity
3879 dependences are all zero in that direction (for fixed
3880 iterations of outer bands).
3882 A representation of the band can be printed using
3884 #include <isl/band.h>
3885 __isl_give isl_printer *isl_printer_print_band(
3886 __isl_take isl_printer *p,
3887 __isl_keep isl_band *band);
3889 =head2 Parametric Vertex Enumeration
3891 The parametric vertex enumeration described in this section
3892 is mainly intended to be used internally and by the C<barvinok>
3895 #include <isl/vertices.h>
3896 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3897 __isl_keep isl_basic_set *bset);
3899 The function C<isl_basic_set_compute_vertices> performs the
3900 actual computation of the parametric vertices and the chamber
3901 decomposition and store the result in an C<isl_vertices> object.
3902 This information can be queried by either iterating over all
3903 the vertices or iterating over all the chambers or cells
3904 and then iterating over all vertices that are active on the chamber.
3906 int isl_vertices_foreach_vertex(
3907 __isl_keep isl_vertices *vertices,
3908 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3911 int isl_vertices_foreach_cell(
3912 __isl_keep isl_vertices *vertices,
3913 int (*fn)(__isl_take isl_cell *cell, void *user),
3915 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3916 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3919 Other operations that can be performed on an C<isl_vertices> object are
3922 isl_ctx *isl_vertices_get_ctx(
3923 __isl_keep isl_vertices *vertices);
3924 int isl_vertices_get_n_vertices(
3925 __isl_keep isl_vertices *vertices);
3926 void isl_vertices_free(__isl_take isl_vertices *vertices);
3928 Vertices can be inspected and destroyed using the following functions.
3930 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3931 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3932 __isl_give isl_basic_set *isl_vertex_get_domain(
3933 __isl_keep isl_vertex *vertex);
3934 __isl_give isl_basic_set *isl_vertex_get_expr(
3935 __isl_keep isl_vertex *vertex);
3936 void isl_vertex_free(__isl_take isl_vertex *vertex);
3938 C<isl_vertex_get_expr> returns a singleton parametric set describing
3939 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3941 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3942 B<rational> basic sets, so they should mainly be used for inspection
3943 and should not be mixed with integer sets.
3945 Chambers can be inspected and destroyed using the following functions.
3947 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3948 __isl_give isl_basic_set *isl_cell_get_domain(
3949 __isl_keep isl_cell *cell);
3950 void isl_cell_free(__isl_take isl_cell *cell);
3954 Although C<isl> is mainly meant to be used as a library,
3955 it also contains some basic applications that use some
3956 of the functionality of C<isl>.
3957 The input may be specified in either the L<isl format>
3958 or the L<PolyLib format>.
3960 =head2 C<isl_polyhedron_sample>
3962 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3963 an integer element of the polyhedron, if there is any.
3964 The first column in the output is the denominator and is always
3965 equal to 1. If the polyhedron contains no integer points,
3966 then a vector of length zero is printed.
3970 C<isl_pip> takes the same input as the C<example> program
3971 from the C<piplib> distribution, i.e., a set of constraints
3972 on the parameters, a line containing only -1 and finally a set
3973 of constraints on a parametric polyhedron.
3974 The coefficients of the parameters appear in the last columns
3975 (but before the final constant column).
3976 The output is the lexicographic minimum of the parametric polyhedron.
3977 As C<isl> currently does not have its own output format, the output
3978 is just a dump of the internal state.
3980 =head2 C<isl_polyhedron_minimize>
3982 C<isl_polyhedron_minimize> computes the minimum of some linear
3983 or affine objective function over the integer points in a polyhedron.
3984 If an affine objective function
3985 is given, then the constant should appear in the last column.
3987 =head2 C<isl_polytope_scan>
3989 Given a polytope, C<isl_polytope_scan> prints
3990 all integer points in the polytope.