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);
604 #include <isl/point.h>
605 __isl_give isl_space *isl_point_get_space(
606 __isl_keep isl_point *pnt);
608 The identifiers or names of the individual dimensions may be set or read off
609 using the following functions.
611 #include <isl/space.h>
612 __isl_give isl_space *isl_space_set_dim_id(
613 __isl_take isl_space *space,
614 enum isl_dim_type type, unsigned pos,
615 __isl_take isl_id *id);
616 int isl_space_has_dim_id(__isl_keep isl_space *space,
617 enum isl_dim_type type, unsigned pos);
618 __isl_give isl_id *isl_space_get_dim_id(
619 __isl_keep isl_space *space,
620 enum isl_dim_type type, unsigned pos);
621 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
622 enum isl_dim_type type, unsigned pos,
623 __isl_keep const char *name);
624 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
625 enum isl_dim_type type, unsigned pos);
627 Note that C<isl_space_get_name> returns a pointer to some internal
628 data structure, so the result can only be used while the
629 corresponding C<isl_space> is alive.
630 Also note that every function that operates on two sets or relations
631 requires that both arguments have the same parameters. This also
632 means that if one of the arguments has named parameters, then the
633 other needs to have named parameters too and the names need to match.
634 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
635 arguments may have different parameters (as long as they are named),
636 in which case the result will have as parameters the union of the parameters of
639 Given the identifier or name of a dimension (typically a parameter),
640 its position can be obtained from the following function.
642 #include <isl/space.h>
643 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
644 enum isl_dim_type type, __isl_keep isl_id *id);
645 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
646 enum isl_dim_type type, const char *name);
648 The identifiers or names of entire spaces may be set or read off
649 using the following functions.
651 #include <isl/space.h>
652 __isl_give isl_space *isl_space_set_tuple_id(
653 __isl_take isl_space *space,
654 enum isl_dim_type type, __isl_take isl_id *id);
655 __isl_give isl_space *isl_space_reset_tuple_id(
656 __isl_take isl_space *space, enum isl_dim_type type);
657 int isl_space_has_tuple_id(__isl_keep isl_space *space,
658 enum isl_dim_type type);
659 __isl_give isl_id *isl_space_get_tuple_id(
660 __isl_keep isl_space *space, enum isl_dim_type type);
661 __isl_give isl_space *isl_space_set_tuple_name(
662 __isl_take isl_space *space,
663 enum isl_dim_type type, const char *s);
664 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
665 enum isl_dim_type type);
667 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
668 or C<isl_dim_set>. As with C<isl_space_get_name>,
669 the C<isl_space_get_tuple_name> function returns a pointer to some internal
671 Binary operations require the corresponding spaces of their arguments
672 to have the same name.
674 Spaces can be nested. In particular, the domain of a set or
675 the domain or range of a relation can be a nested relation.
676 The following functions can be used to construct and deconstruct
679 #include <isl/space.h>
680 int isl_space_is_wrapping(__isl_keep isl_space *space);
681 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
682 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
684 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
685 be the space of a set, while that of
686 C<isl_space_wrap> should be the space of a relation.
687 Conversely, the output of C<isl_space_unwrap> is the space
688 of a relation, while that of C<isl_space_wrap> is the space of a set.
690 Spaces can be created from other spaces
691 using the following functions.
693 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
694 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
695 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
696 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
697 __isl_give isl_space *isl_space_params(
698 __isl_take isl_space *space);
699 __isl_give isl_space *isl_space_set_from_params(
700 __isl_take isl_space *space);
701 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
702 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
703 __isl_take isl_space *right);
704 __isl_give isl_space *isl_space_align_params(
705 __isl_take isl_space *space1, __isl_take isl_space *space2)
706 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
707 enum isl_dim_type type, unsigned pos, unsigned n);
708 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
709 enum isl_dim_type type, unsigned n);
710 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
711 enum isl_dim_type type, unsigned first, unsigned n);
712 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
713 enum isl_dim_type dst_type, unsigned dst_pos,
714 enum isl_dim_type src_type, unsigned src_pos,
716 __isl_give isl_space *isl_space_map_from_set(
717 __isl_take isl_space *space);
718 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
720 Note that if dimensions are added or removed from a space, then
721 the name and the internal structure are lost.
725 A local space is essentially a space with
726 zero or more existentially quantified variables.
727 The local space of a basic set or relation can be obtained
728 using the following functions.
731 __isl_give isl_local_space *isl_basic_set_get_local_space(
732 __isl_keep isl_basic_set *bset);
735 __isl_give isl_local_space *isl_basic_map_get_local_space(
736 __isl_keep isl_basic_map *bmap);
738 A new local space can be created from a space using
740 #include <isl/local_space.h>
741 __isl_give isl_local_space *isl_local_space_from_space(
742 __isl_take isl_space *space);
744 They can be inspected, modified, copied and freed using the following functions.
746 #include <isl/local_space.h>
747 isl_ctx *isl_local_space_get_ctx(
748 __isl_keep isl_local_space *ls);
749 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
750 int isl_local_space_dim(__isl_keep isl_local_space *ls,
751 enum isl_dim_type type);
752 const char *isl_local_space_get_dim_name(
753 __isl_keep isl_local_space *ls,
754 enum isl_dim_type type, unsigned pos);
755 __isl_give isl_local_space *isl_local_space_set_dim_name(
756 __isl_take isl_local_space *ls,
757 enum isl_dim_type type, unsigned pos, const char *s);
758 __isl_give isl_local_space *isl_local_space_set_dim_id(
759 __isl_take isl_local_space *ls,
760 enum isl_dim_type type, unsigned pos,
761 __isl_take isl_id *id);
762 __isl_give isl_space *isl_local_space_get_space(
763 __isl_keep isl_local_space *ls);
764 __isl_give isl_aff *isl_local_space_get_div(
765 __isl_keep isl_local_space *ls, int pos);
766 __isl_give isl_local_space *isl_local_space_copy(
767 __isl_keep isl_local_space *ls);
768 void *isl_local_space_free(__isl_take isl_local_space *ls);
770 Two local spaces can be compared using
772 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
773 __isl_keep isl_local_space *ls2);
775 Local spaces can be created from other local spaces
776 using the following functions.
778 __isl_give isl_local_space *isl_local_space_domain(
779 __isl_take isl_local_space *ls);
780 __isl_give isl_local_space *isl_local_space_from_domain(
781 __isl_take isl_local_space *ls);
782 __isl_give isl_local_space *isl_local_space_add_dims(
783 __isl_take isl_local_space *ls,
784 enum isl_dim_type type, unsigned n);
785 __isl_give isl_local_space *isl_local_space_insert_dims(
786 __isl_take isl_local_space *ls,
787 enum isl_dim_type type, unsigned first, unsigned n);
788 __isl_give isl_local_space *isl_local_space_drop_dims(
789 __isl_take isl_local_space *ls,
790 enum isl_dim_type type, unsigned first, unsigned n);
792 =head2 Input and Output
794 C<isl> supports its own input/output format, which is similar
795 to the C<Omega> format, but also supports the C<PolyLib> format
800 The C<isl> format is similar to that of C<Omega>, but has a different
801 syntax for describing the parameters and allows for the definition
802 of an existentially quantified variable as the integer division
803 of an affine expression.
804 For example, the set of integers C<i> between C<0> and C<n>
805 such that C<i % 10 <= 6> can be described as
807 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
810 A set or relation can have several disjuncts, separated
811 by the keyword C<or>. Each disjunct is either a conjunction
812 of constraints or a projection (C<exists>) of a conjunction
813 of constraints. The constraints are separated by the keyword
816 =head3 C<PolyLib> format
818 If the represented set is a union, then the first line
819 contains a single number representing the number of disjuncts.
820 Otherwise, a line containing the number C<1> is optional.
822 Each disjunct is represented by a matrix of constraints.
823 The first line contains two numbers representing
824 the number of rows and columns,
825 where the number of rows is equal to the number of constraints
826 and the number of columns is equal to two plus the number of variables.
827 The following lines contain the actual rows of the constraint matrix.
828 In each row, the first column indicates whether the constraint
829 is an equality (C<0>) or inequality (C<1>). The final column
830 corresponds to the constant term.
832 If the set is parametric, then the coefficients of the parameters
833 appear in the last columns before the constant column.
834 The coefficients of any existentially quantified variables appear
835 between those of the set variables and those of the parameters.
837 =head3 Extended C<PolyLib> format
839 The extended C<PolyLib> format is nearly identical to the
840 C<PolyLib> format. The only difference is that the line
841 containing the number of rows and columns of a constraint matrix
842 also contains four additional numbers:
843 the number of output dimensions, the number of input dimensions,
844 the number of local dimensions (i.e., the number of existentially
845 quantified variables) and the number of parameters.
846 For sets, the number of ``output'' dimensions is equal
847 to the number of set dimensions, while the number of ``input''
853 __isl_give isl_basic_set *isl_basic_set_read_from_file(
854 isl_ctx *ctx, FILE *input);
855 __isl_give isl_basic_set *isl_basic_set_read_from_str(
856 isl_ctx *ctx, const char *str);
857 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
859 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
863 __isl_give isl_basic_map *isl_basic_map_read_from_file(
864 isl_ctx *ctx, FILE *input);
865 __isl_give isl_basic_map *isl_basic_map_read_from_str(
866 isl_ctx *ctx, const char *str);
867 __isl_give isl_map *isl_map_read_from_file(
868 isl_ctx *ctx, FILE *input);
869 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
872 #include <isl/union_set.h>
873 __isl_give isl_union_set *isl_union_set_read_from_file(
874 isl_ctx *ctx, FILE *input);
875 __isl_give isl_union_set *isl_union_set_read_from_str(
876 isl_ctx *ctx, const char *str);
878 #include <isl/union_map.h>
879 __isl_give isl_union_map *isl_union_map_read_from_file(
880 isl_ctx *ctx, FILE *input);
881 __isl_give isl_union_map *isl_union_map_read_from_str(
882 isl_ctx *ctx, const char *str);
884 The input format is autodetected and may be either the C<PolyLib> format
885 or the C<isl> format.
889 Before anything can be printed, an C<isl_printer> needs to
892 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
894 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
895 void isl_printer_free(__isl_take isl_printer *printer);
896 __isl_give char *isl_printer_get_str(
897 __isl_keep isl_printer *printer);
899 The behavior of the printer can be modified in various ways
901 __isl_give isl_printer *isl_printer_set_output_format(
902 __isl_take isl_printer *p, int output_format);
903 __isl_give isl_printer *isl_printer_set_indent(
904 __isl_take isl_printer *p, int indent);
905 __isl_give isl_printer *isl_printer_indent(
906 __isl_take isl_printer *p, int indent);
907 __isl_give isl_printer *isl_printer_set_prefix(
908 __isl_take isl_printer *p, const char *prefix);
909 __isl_give isl_printer *isl_printer_set_suffix(
910 __isl_take isl_printer *p, const char *suffix);
912 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
913 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
914 and defaults to C<ISL_FORMAT_ISL>.
915 Each line in the output is indented by C<indent> (set by
916 C<isl_printer_set_indent>) spaces
917 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
918 In the C<PolyLib> format output,
919 the coefficients of the existentially quantified variables
920 appear between those of the set variables and those
922 The function C<isl_printer_indent> increases the indentation
923 by the specified amount (which may be negative).
925 To actually print something, use
928 __isl_give isl_printer *isl_printer_print_basic_set(
929 __isl_take isl_printer *printer,
930 __isl_keep isl_basic_set *bset);
931 __isl_give isl_printer *isl_printer_print_set(
932 __isl_take isl_printer *printer,
933 __isl_keep isl_set *set);
936 __isl_give isl_printer *isl_printer_print_basic_map(
937 __isl_take isl_printer *printer,
938 __isl_keep isl_basic_map *bmap);
939 __isl_give isl_printer *isl_printer_print_map(
940 __isl_take isl_printer *printer,
941 __isl_keep isl_map *map);
943 #include <isl/union_set.h>
944 __isl_give isl_printer *isl_printer_print_union_set(
945 __isl_take isl_printer *p,
946 __isl_keep isl_union_set *uset);
948 #include <isl/union_map.h>
949 __isl_give isl_printer *isl_printer_print_union_map(
950 __isl_take isl_printer *p,
951 __isl_keep isl_union_map *umap);
953 When called on a file printer, the following function flushes
954 the file. When called on a string printer, the buffer is cleared.
956 __isl_give isl_printer *isl_printer_flush(
957 __isl_take isl_printer *p);
959 =head2 Creating New Sets and Relations
961 C<isl> has functions for creating some standard sets and relations.
965 =item * Empty sets and relations
967 __isl_give isl_basic_set *isl_basic_set_empty(
968 __isl_take isl_space *space);
969 __isl_give isl_basic_map *isl_basic_map_empty(
970 __isl_take isl_space *space);
971 __isl_give isl_set *isl_set_empty(
972 __isl_take isl_space *space);
973 __isl_give isl_map *isl_map_empty(
974 __isl_take isl_space *space);
975 __isl_give isl_union_set *isl_union_set_empty(
976 __isl_take isl_space *space);
977 __isl_give isl_union_map *isl_union_map_empty(
978 __isl_take isl_space *space);
980 For C<isl_union_set>s and C<isl_union_map>s, the space
981 is only used to specify the parameters.
983 =item * Universe sets and relations
985 __isl_give isl_basic_set *isl_basic_set_universe(
986 __isl_take isl_space *space);
987 __isl_give isl_basic_map *isl_basic_map_universe(
988 __isl_take isl_space *space);
989 __isl_give isl_set *isl_set_universe(
990 __isl_take isl_space *space);
991 __isl_give isl_map *isl_map_universe(
992 __isl_take isl_space *space);
993 __isl_give isl_union_set *isl_union_set_universe(
994 __isl_take isl_union_set *uset);
995 __isl_give isl_union_map *isl_union_map_universe(
996 __isl_take isl_union_map *umap);
998 The sets and relations constructed by the functions above
999 contain all integer values, while those constructed by the
1000 functions below only contain non-negative values.
1002 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1003 __isl_take isl_space *space);
1004 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1005 __isl_take isl_space *space);
1006 __isl_give isl_set *isl_set_nat_universe(
1007 __isl_take isl_space *space);
1008 __isl_give isl_map *isl_map_nat_universe(
1009 __isl_take isl_space *space);
1011 =item * Identity relations
1013 __isl_give isl_basic_map *isl_basic_map_identity(
1014 __isl_take isl_space *space);
1015 __isl_give isl_map *isl_map_identity(
1016 __isl_take isl_space *space);
1018 The number of input and output dimensions in C<space> needs
1021 =item * Lexicographic order
1023 __isl_give isl_map *isl_map_lex_lt(
1024 __isl_take isl_space *set_space);
1025 __isl_give isl_map *isl_map_lex_le(
1026 __isl_take isl_space *set_space);
1027 __isl_give isl_map *isl_map_lex_gt(
1028 __isl_take isl_space *set_space);
1029 __isl_give isl_map *isl_map_lex_ge(
1030 __isl_take isl_space *set_space);
1031 __isl_give isl_map *isl_map_lex_lt_first(
1032 __isl_take isl_space *space, unsigned n);
1033 __isl_give isl_map *isl_map_lex_le_first(
1034 __isl_take isl_space *space, unsigned n);
1035 __isl_give isl_map *isl_map_lex_gt_first(
1036 __isl_take isl_space *space, unsigned n);
1037 __isl_give isl_map *isl_map_lex_ge_first(
1038 __isl_take isl_space *space, unsigned n);
1040 The first four functions take a space for a B<set>
1041 and return relations that express that the elements in the domain
1042 are lexicographically less
1043 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1044 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1045 than the elements in the range.
1046 The last four functions take a space for a map
1047 and return relations that express that the first C<n> dimensions
1048 in the domain are lexicographically less
1049 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1050 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1051 than the first C<n> dimensions in the range.
1055 A basic set or relation can be converted to a set or relation
1056 using the following functions.
1058 __isl_give isl_set *isl_set_from_basic_set(
1059 __isl_take isl_basic_set *bset);
1060 __isl_give isl_map *isl_map_from_basic_map(
1061 __isl_take isl_basic_map *bmap);
1063 Sets and relations can be converted to union sets and relations
1064 using the following functions.
1066 __isl_give isl_union_map *isl_union_map_from_map(
1067 __isl_take isl_map *map);
1068 __isl_give isl_union_set *isl_union_set_from_set(
1069 __isl_take isl_set *set);
1071 The inverse conversions below can only be used if the input
1072 union set or relation is known to contain elements in exactly one
1075 __isl_give isl_set *isl_set_from_union_set(
1076 __isl_take isl_union_set *uset);
1077 __isl_give isl_map *isl_map_from_union_map(
1078 __isl_take isl_union_map *umap);
1080 A zero-dimensional set can be constructed on a given parameter domain
1081 using the following function.
1083 __isl_give isl_set *isl_set_from_params(
1084 __isl_take isl_set *set);
1086 Sets and relations can be copied and freed again using the following
1089 __isl_give isl_basic_set *isl_basic_set_copy(
1090 __isl_keep isl_basic_set *bset);
1091 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1092 __isl_give isl_union_set *isl_union_set_copy(
1093 __isl_keep isl_union_set *uset);
1094 __isl_give isl_basic_map *isl_basic_map_copy(
1095 __isl_keep isl_basic_map *bmap);
1096 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1097 __isl_give isl_union_map *isl_union_map_copy(
1098 __isl_keep isl_union_map *umap);
1099 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1100 void isl_set_free(__isl_take isl_set *set);
1101 void *isl_union_set_free(__isl_take isl_union_set *uset);
1102 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1103 void isl_map_free(__isl_take isl_map *map);
1104 void *isl_union_map_free(__isl_take isl_union_map *umap);
1106 Other sets and relations can be constructed by starting
1107 from a universe set or relation, adding equality and/or
1108 inequality constraints and then projecting out the
1109 existentially quantified variables, if any.
1110 Constraints can be constructed, manipulated and
1111 added to (or removed from) (basic) sets and relations
1112 using the following functions.
1114 #include <isl/constraint.h>
1115 __isl_give isl_constraint *isl_equality_alloc(
1116 __isl_take isl_local_space *ls);
1117 __isl_give isl_constraint *isl_inequality_alloc(
1118 __isl_take isl_local_space *ls);
1119 __isl_give isl_constraint *isl_constraint_set_constant(
1120 __isl_take isl_constraint *constraint, isl_int v);
1121 __isl_give isl_constraint *isl_constraint_set_constant_si(
1122 __isl_take isl_constraint *constraint, int v);
1123 __isl_give isl_constraint *isl_constraint_set_coefficient(
1124 __isl_take isl_constraint *constraint,
1125 enum isl_dim_type type, int pos, isl_int v);
1126 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1127 __isl_take isl_constraint *constraint,
1128 enum isl_dim_type type, int pos, int v);
1129 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1130 __isl_take isl_basic_map *bmap,
1131 __isl_take isl_constraint *constraint);
1132 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1133 __isl_take isl_basic_set *bset,
1134 __isl_take isl_constraint *constraint);
1135 __isl_give isl_map *isl_map_add_constraint(
1136 __isl_take isl_map *map,
1137 __isl_take isl_constraint *constraint);
1138 __isl_give isl_set *isl_set_add_constraint(
1139 __isl_take isl_set *set,
1140 __isl_take isl_constraint *constraint);
1141 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1142 __isl_take isl_basic_set *bset,
1143 __isl_take isl_constraint *constraint);
1145 For example, to create a set containing the even integers
1146 between 10 and 42, you would use the following code.
1149 isl_local_space *ls;
1151 isl_basic_set *bset;
1153 space = isl_space_set_alloc(ctx, 0, 2);
1154 bset = isl_basic_set_universe(isl_space_copy(space));
1155 ls = isl_local_space_from_space(space);
1157 c = isl_equality_alloc(isl_local_space_copy(ls));
1158 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1159 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1160 bset = isl_basic_set_add_constraint(bset, c);
1162 c = isl_inequality_alloc(isl_local_space_copy(ls));
1163 c = isl_constraint_set_constant_si(c, -10);
1164 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1165 bset = isl_basic_set_add_constraint(bset, c);
1167 c = isl_inequality_alloc(ls);
1168 c = isl_constraint_set_constant_si(c, 42);
1169 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1170 bset = isl_basic_set_add_constraint(bset, c);
1172 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1176 isl_basic_set *bset;
1177 bset = isl_basic_set_read_from_str(ctx,
1178 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1180 A basic set or relation can also be constructed from two matrices
1181 describing the equalities and the inequalities.
1183 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1184 __isl_take isl_space *space,
1185 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1186 enum isl_dim_type c1,
1187 enum isl_dim_type c2, enum isl_dim_type c3,
1188 enum isl_dim_type c4);
1189 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1190 __isl_take isl_space *space,
1191 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1192 enum isl_dim_type c1,
1193 enum isl_dim_type c2, enum isl_dim_type c3,
1194 enum isl_dim_type c4, enum isl_dim_type c5);
1196 The C<isl_dim_type> arguments indicate the order in which
1197 different kinds of variables appear in the input matrices
1198 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1199 C<isl_dim_set> and C<isl_dim_div> for sets and
1200 of C<isl_dim_cst>, C<isl_dim_param>,
1201 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1203 A (basic) set or relation can also be constructed from a (piecewise)
1205 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1207 __isl_give isl_basic_map *isl_basic_map_from_aff(
1208 __isl_take isl_aff *aff);
1209 __isl_give isl_set *isl_set_from_pw_aff(
1210 __isl_take isl_pw_aff *pwaff);
1211 __isl_give isl_map *isl_map_from_pw_aff(
1212 __isl_take isl_pw_aff *pwaff);
1213 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1214 __isl_take isl_space *domain_space,
1215 __isl_take isl_aff_list *list);
1217 The C<domain_dim> argument describes the domain of the resulting
1218 basic relation. It is required because the C<list> may consist
1219 of zero affine expressions.
1221 =head2 Inspecting Sets and Relations
1223 Usually, the user should not have to care about the actual constraints
1224 of the sets and maps, but should instead apply the abstract operations
1225 explained in the following sections.
1226 Occasionally, however, it may be required to inspect the individual
1227 coefficients of the constraints. This section explains how to do so.
1228 In these cases, it may also be useful to have C<isl> compute
1229 an explicit representation of the existentially quantified variables.
1231 __isl_give isl_set *isl_set_compute_divs(
1232 __isl_take isl_set *set);
1233 __isl_give isl_map *isl_map_compute_divs(
1234 __isl_take isl_map *map);
1235 __isl_give isl_union_set *isl_union_set_compute_divs(
1236 __isl_take isl_union_set *uset);
1237 __isl_give isl_union_map *isl_union_map_compute_divs(
1238 __isl_take isl_union_map *umap);
1240 This explicit representation defines the existentially quantified
1241 variables as integer divisions of the other variables, possibly
1242 including earlier existentially quantified variables.
1243 An explicitly represented existentially quantified variable therefore
1244 has a unique value when the values of the other variables are known.
1245 If, furthermore, the same existentials, i.e., existentials
1246 with the same explicit representations, should appear in the
1247 same order in each of the disjuncts of a set or map, then the user should call
1248 either of the following functions.
1250 __isl_give isl_set *isl_set_align_divs(
1251 __isl_take isl_set *set);
1252 __isl_give isl_map *isl_map_align_divs(
1253 __isl_take isl_map *map);
1255 Alternatively, the existentially quantified variables can be removed
1256 using the following functions, which compute an overapproximation.
1258 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1259 __isl_take isl_basic_set *bset);
1260 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1261 __isl_take isl_basic_map *bmap);
1262 __isl_give isl_set *isl_set_remove_divs(
1263 __isl_take isl_set *set);
1264 __isl_give isl_map *isl_map_remove_divs(
1265 __isl_take isl_map *map);
1267 To iterate over all the sets or maps in a union set or map, use
1269 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1270 int (*fn)(__isl_take isl_set *set, void *user),
1272 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1273 int (*fn)(__isl_take isl_map *map, void *user),
1276 The number of sets or maps in a union set or map can be obtained
1279 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1280 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1282 To extract the set or map in a given space from a union, use
1284 __isl_give isl_set *isl_union_set_extract_set(
1285 __isl_keep isl_union_set *uset,
1286 __isl_take isl_space *space);
1287 __isl_give isl_map *isl_union_map_extract_map(
1288 __isl_keep isl_union_map *umap,
1289 __isl_take isl_space *space);
1291 To iterate over all the basic sets or maps in a set or map, use
1293 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1294 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1296 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1297 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1300 The callback function C<fn> should return 0 if successful and
1301 -1 if an error occurs. In the latter case, or if any other error
1302 occurs, the above functions will return -1.
1304 It should be noted that C<isl> does not guarantee that
1305 the basic sets or maps passed to C<fn> are disjoint.
1306 If this is required, then the user should call one of
1307 the following functions first.
1309 __isl_give isl_set *isl_set_make_disjoint(
1310 __isl_take isl_set *set);
1311 __isl_give isl_map *isl_map_make_disjoint(
1312 __isl_take isl_map *map);
1314 The number of basic sets in a set can be obtained
1317 int isl_set_n_basic_set(__isl_keep isl_set *set);
1319 To iterate over the constraints of a basic set or map, use
1321 #include <isl/constraint.h>
1323 int isl_basic_map_foreach_constraint(
1324 __isl_keep isl_basic_map *bmap,
1325 int (*fn)(__isl_take isl_constraint *c, void *user),
1327 void *isl_constraint_free(__isl_take isl_constraint *c);
1329 Again, the callback function C<fn> should return 0 if successful and
1330 -1 if an error occurs. In the latter case, or if any other error
1331 occurs, the above functions will return -1.
1332 The constraint C<c> represents either an equality or an inequality.
1333 Use the following function to find out whether a constraint
1334 represents an equality. If not, it represents an inequality.
1336 int isl_constraint_is_equality(
1337 __isl_keep isl_constraint *constraint);
1339 The coefficients of the constraints can be inspected using
1340 the following functions.
1342 void isl_constraint_get_constant(
1343 __isl_keep isl_constraint *constraint, isl_int *v);
1344 void isl_constraint_get_coefficient(
1345 __isl_keep isl_constraint *constraint,
1346 enum isl_dim_type type, int pos, isl_int *v);
1347 int isl_constraint_involves_dims(
1348 __isl_keep isl_constraint *constraint,
1349 enum isl_dim_type type, unsigned first, unsigned n);
1351 The explicit representations of the existentially quantified
1352 variables can be inspected using the following function.
1353 Note that the user is only allowed to use this function
1354 if the inspected set or map is the result of a call
1355 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1356 The existentially quantified variable is equal to the floor
1357 of the returned affine expression. The affine expression
1358 itself can be inspected using the functions in
1359 L<"Piecewise Quasi Affine Expressions">.
1361 __isl_give isl_aff *isl_constraint_get_div(
1362 __isl_keep isl_constraint *constraint, int pos);
1364 To obtain the constraints of a basic set or map in matrix
1365 form, use the following functions.
1367 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1368 __isl_keep isl_basic_set *bset,
1369 enum isl_dim_type c1, enum isl_dim_type c2,
1370 enum isl_dim_type c3, enum isl_dim_type c4);
1371 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1372 __isl_keep isl_basic_set *bset,
1373 enum isl_dim_type c1, enum isl_dim_type c2,
1374 enum isl_dim_type c3, enum isl_dim_type c4);
1375 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1376 __isl_keep isl_basic_map *bmap,
1377 enum isl_dim_type c1,
1378 enum isl_dim_type c2, enum isl_dim_type c3,
1379 enum isl_dim_type c4, enum isl_dim_type c5);
1380 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1381 __isl_keep isl_basic_map *bmap,
1382 enum isl_dim_type c1,
1383 enum isl_dim_type c2, enum isl_dim_type c3,
1384 enum isl_dim_type c4, enum isl_dim_type c5);
1386 The C<isl_dim_type> arguments dictate the order in which
1387 different kinds of variables appear in the resulting matrix
1388 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1389 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1391 The number of parameters, input, output or set dimensions can
1392 be obtained using the following functions.
1394 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1395 enum isl_dim_type type);
1396 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1397 enum isl_dim_type type);
1398 unsigned isl_set_dim(__isl_keep isl_set *set,
1399 enum isl_dim_type type);
1400 unsigned isl_map_dim(__isl_keep isl_map *map,
1401 enum isl_dim_type type);
1403 To check whether the description of a set or relation depends
1404 on one or more given dimensions, it is not necessary to iterate over all
1405 constraints. Instead the following functions can be used.
1407 int isl_basic_set_involves_dims(
1408 __isl_keep isl_basic_set *bset,
1409 enum isl_dim_type type, unsigned first, unsigned n);
1410 int isl_set_involves_dims(__isl_keep isl_set *set,
1411 enum isl_dim_type type, unsigned first, unsigned n);
1412 int isl_basic_map_involves_dims(
1413 __isl_keep isl_basic_map *bmap,
1414 enum isl_dim_type type, unsigned first, unsigned n);
1415 int isl_map_involves_dims(__isl_keep isl_map *map,
1416 enum isl_dim_type type, unsigned first, unsigned n);
1418 Similarly, the following functions can be used to check whether
1419 a given dimension is involved in any lower or upper bound.
1421 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1422 enum isl_dim_type type, unsigned pos);
1423 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1424 enum isl_dim_type type, unsigned pos);
1426 The identifiers or names of the domain and range spaces of a set
1427 or relation can be read off or set using the following functions.
1429 __isl_give isl_set *isl_set_set_tuple_id(
1430 __isl_take isl_set *set, __isl_take isl_id *id);
1431 __isl_give isl_set *isl_set_reset_tuple_id(
1432 __isl_take isl_set *set);
1433 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1434 __isl_give isl_id *isl_set_get_tuple_id(
1435 __isl_keep isl_set *set);
1436 __isl_give isl_map *isl_map_set_tuple_id(
1437 __isl_take isl_map *map, enum isl_dim_type type,
1438 __isl_take isl_id *id);
1439 __isl_give isl_map *isl_map_reset_tuple_id(
1440 __isl_take isl_map *map, enum isl_dim_type type);
1441 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1442 enum isl_dim_type type);
1443 __isl_give isl_id *isl_map_get_tuple_id(
1444 __isl_keep isl_map *map, enum isl_dim_type type);
1446 const char *isl_basic_set_get_tuple_name(
1447 __isl_keep isl_basic_set *bset);
1448 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1449 __isl_take isl_basic_set *set, const char *s);
1450 const char *isl_set_get_tuple_name(
1451 __isl_keep isl_set *set);
1452 const char *isl_basic_map_get_tuple_name(
1453 __isl_keep isl_basic_map *bmap,
1454 enum isl_dim_type type);
1455 const char *isl_map_get_tuple_name(
1456 __isl_keep isl_map *map,
1457 enum isl_dim_type type);
1459 As with C<isl_space_get_tuple_name>, the value returned points to
1460 an internal data structure.
1461 The identifiers, positions or names of individual dimensions can be
1462 read off using the following functions.
1464 __isl_give isl_set *isl_set_set_dim_id(
1465 __isl_take isl_set *set, enum isl_dim_type type,
1466 unsigned pos, __isl_take isl_id *id);
1467 int isl_set_has_dim_id(__isl_keep isl_set *set,
1468 enum isl_dim_type type, unsigned pos);
1469 __isl_give isl_id *isl_set_get_dim_id(
1470 __isl_keep isl_set *set, enum isl_dim_type type,
1472 int isl_basic_map_has_dim_id(
1473 __isl_keep isl_basic_map *bmap,
1474 enum isl_dim_type type, unsigned pos);
1475 __isl_give isl_map *isl_map_set_dim_id(
1476 __isl_take isl_map *map, enum isl_dim_type type,
1477 unsigned pos, __isl_take isl_id *id);
1478 int isl_map_has_dim_id(__isl_keep isl_map *map,
1479 enum isl_dim_type type, unsigned pos);
1480 __isl_give isl_id *isl_map_get_dim_id(
1481 __isl_keep isl_map *map, enum isl_dim_type type,
1484 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1485 enum isl_dim_type type, __isl_keep isl_id *id);
1486 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1487 enum isl_dim_type type, __isl_keep isl_id *id);
1488 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1489 enum isl_dim_type type, const char *name);
1491 const char *isl_constraint_get_dim_name(
1492 __isl_keep isl_constraint *constraint,
1493 enum isl_dim_type type, unsigned pos);
1494 const char *isl_basic_set_get_dim_name(
1495 __isl_keep isl_basic_set *bset,
1496 enum isl_dim_type type, unsigned pos);
1497 const char *isl_set_get_dim_name(
1498 __isl_keep isl_set *set,
1499 enum isl_dim_type type, unsigned pos);
1500 const char *isl_basic_map_get_dim_name(
1501 __isl_keep isl_basic_map *bmap,
1502 enum isl_dim_type type, unsigned pos);
1503 const char *isl_map_get_dim_name(
1504 __isl_keep isl_map *map,
1505 enum isl_dim_type type, unsigned pos);
1507 These functions are mostly useful to obtain the identifiers, positions
1508 or names of the parameters. Identifiers of individual dimensions are
1509 essentially only useful for printing. They are ignored by all other
1510 operations and may not be preserved across those operations.
1514 =head3 Unary Properties
1520 The following functions test whether the given set or relation
1521 contains any integer points. The ``plain'' variants do not perform
1522 any computations, but simply check if the given set or relation
1523 is already known to be empty.
1525 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1526 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1527 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1528 int isl_set_is_empty(__isl_keep isl_set *set);
1529 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1530 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1531 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1532 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1533 int isl_map_is_empty(__isl_keep isl_map *map);
1534 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1536 =item * Universality
1538 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1539 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1540 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1542 =item * Single-valuedness
1544 int isl_map_is_single_valued(__isl_keep isl_map *map);
1545 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1549 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1550 int isl_map_is_injective(__isl_keep isl_map *map);
1551 int isl_union_map_plain_is_injective(
1552 __isl_keep isl_union_map *umap);
1553 int isl_union_map_is_injective(
1554 __isl_keep isl_union_map *umap);
1558 int isl_map_is_bijective(__isl_keep isl_map *map);
1559 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1563 int isl_basic_map_plain_is_fixed(
1564 __isl_keep isl_basic_map *bmap,
1565 enum isl_dim_type type, unsigned pos,
1567 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1568 enum isl_dim_type type, unsigned pos,
1570 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1571 enum isl_dim_type type, unsigned pos,
1574 Check if the relation obviously lies on a hyperplane where the given dimension
1575 has a fixed value and if so, return that value in C<*val>.
1579 To check whether a set is a parameter domain, use this function:
1581 int isl_set_is_params(__isl_keep isl_set *set);
1585 The following functions check whether the domain of the given
1586 (basic) set is a wrapped relation.
1588 int isl_basic_set_is_wrapping(
1589 __isl_keep isl_basic_set *bset);
1590 int isl_set_is_wrapping(__isl_keep isl_set *set);
1592 =item * Internal Product
1594 int isl_basic_map_can_zip(
1595 __isl_keep isl_basic_map *bmap);
1596 int isl_map_can_zip(__isl_keep isl_map *map);
1598 Check whether the product of domain and range of the given relation
1600 i.e., whether both domain and range are nested relations.
1604 =head3 Binary Properties
1610 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1611 __isl_keep isl_set *set2);
1612 int isl_set_is_equal(__isl_keep isl_set *set1,
1613 __isl_keep isl_set *set2);
1614 int isl_union_set_is_equal(
1615 __isl_keep isl_union_set *uset1,
1616 __isl_keep isl_union_set *uset2);
1617 int isl_basic_map_is_equal(
1618 __isl_keep isl_basic_map *bmap1,
1619 __isl_keep isl_basic_map *bmap2);
1620 int isl_map_is_equal(__isl_keep isl_map *map1,
1621 __isl_keep isl_map *map2);
1622 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1623 __isl_keep isl_map *map2);
1624 int isl_union_map_is_equal(
1625 __isl_keep isl_union_map *umap1,
1626 __isl_keep isl_union_map *umap2);
1628 =item * Disjointness
1630 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1631 __isl_keep isl_set *set2);
1635 int isl_set_is_subset(__isl_keep isl_set *set1,
1636 __isl_keep isl_set *set2);
1637 int isl_set_is_strict_subset(
1638 __isl_keep isl_set *set1,
1639 __isl_keep isl_set *set2);
1640 int isl_union_set_is_subset(
1641 __isl_keep isl_union_set *uset1,
1642 __isl_keep isl_union_set *uset2);
1643 int isl_union_set_is_strict_subset(
1644 __isl_keep isl_union_set *uset1,
1645 __isl_keep isl_union_set *uset2);
1646 int isl_basic_map_is_subset(
1647 __isl_keep isl_basic_map *bmap1,
1648 __isl_keep isl_basic_map *bmap2);
1649 int isl_basic_map_is_strict_subset(
1650 __isl_keep isl_basic_map *bmap1,
1651 __isl_keep isl_basic_map *bmap2);
1652 int isl_map_is_subset(
1653 __isl_keep isl_map *map1,
1654 __isl_keep isl_map *map2);
1655 int isl_map_is_strict_subset(
1656 __isl_keep isl_map *map1,
1657 __isl_keep isl_map *map2);
1658 int isl_union_map_is_subset(
1659 __isl_keep isl_union_map *umap1,
1660 __isl_keep isl_union_map *umap2);
1661 int isl_union_map_is_strict_subset(
1662 __isl_keep isl_union_map *umap1,
1663 __isl_keep isl_union_map *umap2);
1667 =head2 Unary Operations
1673 __isl_give isl_set *isl_set_complement(
1674 __isl_take isl_set *set);
1678 __isl_give isl_basic_map *isl_basic_map_reverse(
1679 __isl_take isl_basic_map *bmap);
1680 __isl_give isl_map *isl_map_reverse(
1681 __isl_take isl_map *map);
1682 __isl_give isl_union_map *isl_union_map_reverse(
1683 __isl_take isl_union_map *umap);
1687 __isl_give isl_basic_set *isl_basic_set_project_out(
1688 __isl_take isl_basic_set *bset,
1689 enum isl_dim_type type, unsigned first, unsigned n);
1690 __isl_give isl_basic_map *isl_basic_map_project_out(
1691 __isl_take isl_basic_map *bmap,
1692 enum isl_dim_type type, unsigned first, unsigned n);
1693 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1694 enum isl_dim_type type, unsigned first, unsigned n);
1695 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1696 enum isl_dim_type type, unsigned first, unsigned n);
1697 __isl_give isl_basic_set *isl_basic_set_params(
1698 __isl_take isl_basic_set *bset);
1699 __isl_give isl_basic_set *isl_basic_map_domain(
1700 __isl_take isl_basic_map *bmap);
1701 __isl_give isl_basic_set *isl_basic_map_range(
1702 __isl_take isl_basic_map *bmap);
1703 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1704 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1705 __isl_give isl_set *isl_map_domain(
1706 __isl_take isl_map *bmap);
1707 __isl_give isl_set *isl_map_range(
1708 __isl_take isl_map *map);
1709 __isl_give isl_union_set *isl_union_map_domain(
1710 __isl_take isl_union_map *umap);
1711 __isl_give isl_union_set *isl_union_map_range(
1712 __isl_take isl_union_map *umap);
1714 __isl_give isl_basic_map *isl_basic_map_domain_map(
1715 __isl_take isl_basic_map *bmap);
1716 __isl_give isl_basic_map *isl_basic_map_range_map(
1717 __isl_take isl_basic_map *bmap);
1718 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1719 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1720 __isl_give isl_union_map *isl_union_map_domain_map(
1721 __isl_take isl_union_map *umap);
1722 __isl_give isl_union_map *isl_union_map_range_map(
1723 __isl_take isl_union_map *umap);
1725 The functions above construct a (basic, regular or union) relation
1726 that maps (a wrapped version of) the input relation to its domain or range.
1730 __isl_give isl_set *isl_set_eliminate(
1731 __isl_take isl_set *set, enum isl_dim_type type,
1732 unsigned first, unsigned n);
1733 __isl_give isl_basic_map *isl_basic_map_eliminate(
1734 __isl_take isl_basic_map *bmap,
1735 enum isl_dim_type type,
1736 unsigned first, unsigned n);
1738 Eliminate the coefficients for the given dimensions from the constraints,
1739 without removing the dimensions.
1743 __isl_give isl_basic_set *isl_basic_set_fix(
1744 __isl_take isl_basic_set *bset,
1745 enum isl_dim_type type, unsigned pos,
1747 __isl_give isl_basic_set *isl_basic_set_fix_si(
1748 __isl_take isl_basic_set *bset,
1749 enum isl_dim_type type, unsigned pos, int value);
1750 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1751 enum isl_dim_type type, unsigned pos,
1753 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1754 enum isl_dim_type type, unsigned pos, int value);
1755 __isl_give isl_basic_map *isl_basic_map_fix_si(
1756 __isl_take isl_basic_map *bmap,
1757 enum isl_dim_type type, unsigned pos, int value);
1758 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1759 enum isl_dim_type type, unsigned pos, int value);
1761 Intersect the set or relation with the hyperplane where the given
1762 dimension has the fixed given value.
1764 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1765 enum isl_dim_type type1, int pos1,
1766 enum isl_dim_type type2, int pos2);
1767 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1768 enum isl_dim_type type1, int pos1,
1769 enum isl_dim_type type2, int pos2);
1771 Intersect the set or relation with the hyperplane where the given
1772 dimensions are equal to each other.
1774 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1775 enum isl_dim_type type1, int pos1,
1776 enum isl_dim_type type2, int pos2);
1778 Intersect the relation with the hyperplane where the given
1779 dimensions have opposite values.
1783 __isl_give isl_map *isl_set_identity(
1784 __isl_take isl_set *set);
1785 __isl_give isl_union_map *isl_union_set_identity(
1786 __isl_take isl_union_set *uset);
1788 Construct an identity relation on the given (union) set.
1792 __isl_give isl_basic_set *isl_basic_map_deltas(
1793 __isl_take isl_basic_map *bmap);
1794 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1795 __isl_give isl_union_set *isl_union_map_deltas(
1796 __isl_take isl_union_map *umap);
1798 These functions return a (basic) set containing the differences
1799 between image elements and corresponding domain elements in the input.
1801 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1802 __isl_take isl_basic_map *bmap);
1803 __isl_give isl_map *isl_map_deltas_map(
1804 __isl_take isl_map *map);
1805 __isl_give isl_union_map *isl_union_map_deltas_map(
1806 __isl_take isl_union_map *umap);
1808 The functions above construct a (basic, regular or union) relation
1809 that maps (a wrapped version of) the input relation to its delta set.
1813 Simplify the representation of a set or relation by trying
1814 to combine pairs of basic sets or relations into a single
1815 basic set or relation.
1817 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1818 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1819 __isl_give isl_union_set *isl_union_set_coalesce(
1820 __isl_take isl_union_set *uset);
1821 __isl_give isl_union_map *isl_union_map_coalesce(
1822 __isl_take isl_union_map *umap);
1824 =item * Detecting equalities
1826 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1827 __isl_take isl_basic_set *bset);
1828 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1829 __isl_take isl_basic_map *bmap);
1830 __isl_give isl_set *isl_set_detect_equalities(
1831 __isl_take isl_set *set);
1832 __isl_give isl_map *isl_map_detect_equalities(
1833 __isl_take isl_map *map);
1834 __isl_give isl_union_set *isl_union_set_detect_equalities(
1835 __isl_take isl_union_set *uset);
1836 __isl_give isl_union_map *isl_union_map_detect_equalities(
1837 __isl_take isl_union_map *umap);
1839 Simplify the representation of a set or relation by detecting implicit
1842 =item * Removing redundant constraints
1844 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1845 __isl_take isl_basic_set *bset);
1846 __isl_give isl_set *isl_set_remove_redundancies(
1847 __isl_take isl_set *set);
1848 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1849 __isl_take isl_basic_map *bmap);
1850 __isl_give isl_map *isl_map_remove_redundancies(
1851 __isl_take isl_map *map);
1855 __isl_give isl_basic_set *isl_set_convex_hull(
1856 __isl_take isl_set *set);
1857 __isl_give isl_basic_map *isl_map_convex_hull(
1858 __isl_take isl_map *map);
1860 If the input set or relation has any existentially quantified
1861 variables, then the result of these operations is currently undefined.
1865 __isl_give isl_basic_set *isl_set_simple_hull(
1866 __isl_take isl_set *set);
1867 __isl_give isl_basic_map *isl_map_simple_hull(
1868 __isl_take isl_map *map);
1869 __isl_give isl_union_map *isl_union_map_simple_hull(
1870 __isl_take isl_union_map *umap);
1872 These functions compute a single basic set or relation
1873 that contains the whole input set or relation.
1874 In particular, the output is described by translates
1875 of the constraints describing the basic sets or relations in the input.
1879 (See \autoref{s:simple hull}.)
1885 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1886 __isl_take isl_basic_set *bset);
1887 __isl_give isl_basic_set *isl_set_affine_hull(
1888 __isl_take isl_set *set);
1889 __isl_give isl_union_set *isl_union_set_affine_hull(
1890 __isl_take isl_union_set *uset);
1891 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1892 __isl_take isl_basic_map *bmap);
1893 __isl_give isl_basic_map *isl_map_affine_hull(
1894 __isl_take isl_map *map);
1895 __isl_give isl_union_map *isl_union_map_affine_hull(
1896 __isl_take isl_union_map *umap);
1898 In case of union sets and relations, the affine hull is computed
1901 =item * Polyhedral hull
1903 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1904 __isl_take isl_set *set);
1905 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1906 __isl_take isl_map *map);
1907 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1908 __isl_take isl_union_set *uset);
1909 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1910 __isl_take isl_union_map *umap);
1912 These functions compute a single basic set or relation
1913 not involving any existentially quantified variables
1914 that contains the whole input set or relation.
1915 In case of union sets and relations, the polyhedral hull is computed
1918 =item * Optimization
1920 #include <isl/ilp.h>
1921 enum isl_lp_result isl_basic_set_max(
1922 __isl_keep isl_basic_set *bset,
1923 __isl_keep isl_aff *obj, isl_int *opt)
1924 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1925 __isl_keep isl_aff *obj, isl_int *opt);
1926 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1927 __isl_keep isl_aff *obj, isl_int *opt);
1929 Compute the minimum or maximum of the integer affine expression C<obj>
1930 over the points in C<set>, returning the result in C<opt>.
1931 The return value may be one of C<isl_lp_error>,
1932 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1934 =item * Parametric optimization
1936 __isl_give isl_pw_aff *isl_set_dim_min(
1937 __isl_take isl_set *set, int pos);
1938 __isl_give isl_pw_aff *isl_set_dim_max(
1939 __isl_take isl_set *set, int pos);
1940 __isl_give isl_pw_aff *isl_map_dim_max(
1941 __isl_take isl_map *map, int pos);
1943 Compute the minimum or maximum of the given set or output dimension
1944 as a function of the parameters (and input dimensions), but independently
1945 of the other set or output dimensions.
1946 For lexicographic optimization, see L<"Lexicographic Optimization">.
1950 The following functions compute either the set of (rational) coefficient
1951 values of valid constraints for the given set or the set of (rational)
1952 values satisfying the constraints with coefficients from the given set.
1953 Internally, these two sets of functions perform essentially the
1954 same operations, except that the set of coefficients is assumed to
1955 be a cone, while the set of values may be any polyhedron.
1956 The current implementation is based on the Farkas lemma and
1957 Fourier-Motzkin elimination, but this may change or be made optional
1958 in future. In particular, future implementations may use different
1959 dualization algorithms or skip the elimination step.
1961 __isl_give isl_basic_set *isl_basic_set_coefficients(
1962 __isl_take isl_basic_set *bset);
1963 __isl_give isl_basic_set *isl_set_coefficients(
1964 __isl_take isl_set *set);
1965 __isl_give isl_union_set *isl_union_set_coefficients(
1966 __isl_take isl_union_set *bset);
1967 __isl_give isl_basic_set *isl_basic_set_solutions(
1968 __isl_take isl_basic_set *bset);
1969 __isl_give isl_basic_set *isl_set_solutions(
1970 __isl_take isl_set *set);
1971 __isl_give isl_union_set *isl_union_set_solutions(
1972 __isl_take isl_union_set *bset);
1976 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1978 __isl_give isl_union_map *isl_union_map_power(
1979 __isl_take isl_union_map *umap, int *exact);
1981 Compute a parametric representation for all positive powers I<k> of C<map>.
1982 The result maps I<k> to a nested relation corresponding to the
1983 I<k>th power of C<map>.
1984 The result may be an overapproximation. If the result is known to be exact,
1985 then C<*exact> is set to C<1>.
1987 =item * Transitive closure
1989 __isl_give isl_map *isl_map_transitive_closure(
1990 __isl_take isl_map *map, int *exact);
1991 __isl_give isl_union_map *isl_union_map_transitive_closure(
1992 __isl_take isl_union_map *umap, int *exact);
1994 Compute the transitive closure of C<map>.
1995 The result may be an overapproximation. If the result is known to be exact,
1996 then C<*exact> is set to C<1>.
1998 =item * Reaching path lengths
2000 __isl_give isl_map *isl_map_reaching_path_lengths(
2001 __isl_take isl_map *map, int *exact);
2003 Compute a relation that maps each element in the range of C<map>
2004 to the lengths of all paths composed of edges in C<map> that
2005 end up in the given element.
2006 The result may be an overapproximation. If the result is known to be exact,
2007 then C<*exact> is set to C<1>.
2008 To compute the I<maximal> path length, the resulting relation
2009 should be postprocessed by C<isl_map_lexmax>.
2010 In particular, if the input relation is a dependence relation
2011 (mapping sources to sinks), then the maximal path length corresponds
2012 to the free schedule.
2013 Note, however, that C<isl_map_lexmax> expects the maximum to be
2014 finite, so if the path lengths are unbounded (possibly due to
2015 the overapproximation), then you will get an error message.
2019 __isl_give isl_basic_set *isl_basic_map_wrap(
2020 __isl_take isl_basic_map *bmap);
2021 __isl_give isl_set *isl_map_wrap(
2022 __isl_take isl_map *map);
2023 __isl_give isl_union_set *isl_union_map_wrap(
2024 __isl_take isl_union_map *umap);
2025 __isl_give isl_basic_map *isl_basic_set_unwrap(
2026 __isl_take isl_basic_set *bset);
2027 __isl_give isl_map *isl_set_unwrap(
2028 __isl_take isl_set *set);
2029 __isl_give isl_union_map *isl_union_set_unwrap(
2030 __isl_take isl_union_set *uset);
2034 Remove any internal structure of domain (and range) of the given
2035 set or relation. If there is any such internal structure in the input,
2036 then the name of the space is also removed.
2038 __isl_give isl_basic_set *isl_basic_set_flatten(
2039 __isl_take isl_basic_set *bset);
2040 __isl_give isl_set *isl_set_flatten(
2041 __isl_take isl_set *set);
2042 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2043 __isl_take isl_basic_map *bmap);
2044 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2045 __isl_take isl_basic_map *bmap);
2046 __isl_give isl_map *isl_map_flatten_range(
2047 __isl_take isl_map *map);
2048 __isl_give isl_map *isl_map_flatten_domain(
2049 __isl_take isl_map *map);
2050 __isl_give isl_basic_map *isl_basic_map_flatten(
2051 __isl_take isl_basic_map *bmap);
2052 __isl_give isl_map *isl_map_flatten(
2053 __isl_take isl_map *map);
2055 __isl_give isl_map *isl_set_flatten_map(
2056 __isl_take isl_set *set);
2058 The function above constructs a relation
2059 that maps the input set to a flattened version of the set.
2063 Lift the input set to a space with extra dimensions corresponding
2064 to the existentially quantified variables in the input.
2065 In particular, the result lives in a wrapped map where the domain
2066 is the original space and the range corresponds to the original
2067 existentially quantified variables.
2069 __isl_give isl_basic_set *isl_basic_set_lift(
2070 __isl_take isl_basic_set *bset);
2071 __isl_give isl_set *isl_set_lift(
2072 __isl_take isl_set *set);
2073 __isl_give isl_union_set *isl_union_set_lift(
2074 __isl_take isl_union_set *uset);
2076 =item * Internal Product
2078 __isl_give isl_basic_map *isl_basic_map_zip(
2079 __isl_take isl_basic_map *bmap);
2080 __isl_give isl_map *isl_map_zip(
2081 __isl_take isl_map *map);
2082 __isl_give isl_union_map *isl_union_map_zip(
2083 __isl_take isl_union_map *umap);
2085 Given a relation with nested relations for domain and range,
2086 interchange the range of the domain with the domain of the range.
2088 =item * Aligning parameters
2090 __isl_give isl_set *isl_set_align_params(
2091 __isl_take isl_set *set,
2092 __isl_take isl_space *model);
2093 __isl_give isl_map *isl_map_align_params(
2094 __isl_take isl_map *map,
2095 __isl_take isl_space *model);
2097 Change the order of the parameters of the given set or relation
2098 such that the first parameters match those of C<model>.
2099 This may involve the introduction of extra parameters.
2100 All parameters need to be named.
2102 =item * Dimension manipulation
2104 __isl_give isl_set *isl_set_add_dims(
2105 __isl_take isl_set *set,
2106 enum isl_dim_type type, unsigned n);
2107 __isl_give isl_map *isl_map_add_dims(
2108 __isl_take isl_map *map,
2109 enum isl_dim_type type, unsigned n);
2110 __isl_give isl_set *isl_set_insert_dims(
2111 __isl_take isl_set *set,
2112 enum isl_dim_type type, unsigned pos, unsigned n);
2113 __isl_give isl_map *isl_map_insert_dims(
2114 __isl_take isl_map *map,
2115 enum isl_dim_type type, unsigned pos, unsigned n);
2116 __isl_give isl_basic_set *isl_basic_set_move_dims(
2117 __isl_take isl_basic_set *bset,
2118 enum isl_dim_type dst_type, unsigned dst_pos,
2119 enum isl_dim_type src_type, unsigned src_pos,
2121 __isl_give isl_basic_map *isl_basic_map_move_dims(
2122 __isl_take isl_basic_map *bmap,
2123 enum isl_dim_type dst_type, unsigned dst_pos,
2124 enum isl_dim_type src_type, unsigned src_pos,
2126 __isl_give isl_set *isl_set_move_dims(
2127 __isl_take isl_set *set,
2128 enum isl_dim_type dst_type, unsigned dst_pos,
2129 enum isl_dim_type src_type, unsigned src_pos,
2131 __isl_give isl_map *isl_map_move_dims(
2132 __isl_take isl_map *map,
2133 enum isl_dim_type dst_type, unsigned dst_pos,
2134 enum isl_dim_type src_type, unsigned src_pos,
2137 It is usually not advisable to directly change the (input or output)
2138 space of a set or a relation as this removes the name and the internal
2139 structure of the space. However, the above functions can be useful
2140 to add new parameters, assuming
2141 C<isl_set_align_params> and C<isl_map_align_params>
2146 =head2 Binary Operations
2148 The two arguments of a binary operation not only need to live
2149 in the same C<isl_ctx>, they currently also need to have
2150 the same (number of) parameters.
2152 =head3 Basic Operations
2156 =item * Intersection
2158 __isl_give isl_basic_set *isl_basic_set_intersect(
2159 __isl_take isl_basic_set *bset1,
2160 __isl_take isl_basic_set *bset2);
2161 __isl_give isl_set *isl_set_intersect_params(
2162 __isl_take isl_set *set,
2163 __isl_take isl_set *params);
2164 __isl_give isl_set *isl_set_intersect(
2165 __isl_take isl_set *set1,
2166 __isl_take isl_set *set2);
2167 __isl_give isl_union_set *isl_union_set_intersect(
2168 __isl_take isl_union_set *uset1,
2169 __isl_take isl_union_set *uset2);
2170 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2171 __isl_take isl_basic_map *bmap,
2172 __isl_take isl_basic_set *bset);
2173 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2174 __isl_take isl_basic_map *bmap,
2175 __isl_take isl_basic_set *bset);
2176 __isl_give isl_basic_map *isl_basic_map_intersect(
2177 __isl_take isl_basic_map *bmap1,
2178 __isl_take isl_basic_map *bmap2);
2179 __isl_give isl_map *isl_map_intersect_params(
2180 __isl_take isl_map *map,
2181 __isl_take isl_set *params);
2182 __isl_give isl_map *isl_map_intersect_domain(
2183 __isl_take isl_map *map,
2184 __isl_take isl_set *set);
2185 __isl_give isl_map *isl_map_intersect_range(
2186 __isl_take isl_map *map,
2187 __isl_take isl_set *set);
2188 __isl_give isl_map *isl_map_intersect(
2189 __isl_take isl_map *map1,
2190 __isl_take isl_map *map2);
2191 __isl_give isl_union_map *isl_union_map_intersect_domain(
2192 __isl_take isl_union_map *umap,
2193 __isl_take isl_union_set *uset);
2194 __isl_give isl_union_map *isl_union_map_intersect_range(
2195 __isl_take isl_union_map *umap,
2196 __isl_take isl_union_set *uset);
2197 __isl_give isl_union_map *isl_union_map_intersect(
2198 __isl_take isl_union_map *umap1,
2199 __isl_take isl_union_map *umap2);
2203 __isl_give isl_set *isl_basic_set_union(
2204 __isl_take isl_basic_set *bset1,
2205 __isl_take isl_basic_set *bset2);
2206 __isl_give isl_map *isl_basic_map_union(
2207 __isl_take isl_basic_map *bmap1,
2208 __isl_take isl_basic_map *bmap2);
2209 __isl_give isl_set *isl_set_union(
2210 __isl_take isl_set *set1,
2211 __isl_take isl_set *set2);
2212 __isl_give isl_map *isl_map_union(
2213 __isl_take isl_map *map1,
2214 __isl_take isl_map *map2);
2215 __isl_give isl_union_set *isl_union_set_union(
2216 __isl_take isl_union_set *uset1,
2217 __isl_take isl_union_set *uset2);
2218 __isl_give isl_union_map *isl_union_map_union(
2219 __isl_take isl_union_map *umap1,
2220 __isl_take isl_union_map *umap2);
2222 =item * Set difference
2224 __isl_give isl_set *isl_set_subtract(
2225 __isl_take isl_set *set1,
2226 __isl_take isl_set *set2);
2227 __isl_give isl_map *isl_map_subtract(
2228 __isl_take isl_map *map1,
2229 __isl_take isl_map *map2);
2230 __isl_give isl_union_set *isl_union_set_subtract(
2231 __isl_take isl_union_set *uset1,
2232 __isl_take isl_union_set *uset2);
2233 __isl_give isl_union_map *isl_union_map_subtract(
2234 __isl_take isl_union_map *umap1,
2235 __isl_take isl_union_map *umap2);
2239 __isl_give isl_basic_set *isl_basic_set_apply(
2240 __isl_take isl_basic_set *bset,
2241 __isl_take isl_basic_map *bmap);
2242 __isl_give isl_set *isl_set_apply(
2243 __isl_take isl_set *set,
2244 __isl_take isl_map *map);
2245 __isl_give isl_union_set *isl_union_set_apply(
2246 __isl_take isl_union_set *uset,
2247 __isl_take isl_union_map *umap);
2248 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2249 __isl_take isl_basic_map *bmap1,
2250 __isl_take isl_basic_map *bmap2);
2251 __isl_give isl_basic_map *isl_basic_map_apply_range(
2252 __isl_take isl_basic_map *bmap1,
2253 __isl_take isl_basic_map *bmap2);
2254 __isl_give isl_map *isl_map_apply_domain(
2255 __isl_take isl_map *map1,
2256 __isl_take isl_map *map2);
2257 __isl_give isl_union_map *isl_union_map_apply_domain(
2258 __isl_take isl_union_map *umap1,
2259 __isl_take isl_union_map *umap2);
2260 __isl_give isl_map *isl_map_apply_range(
2261 __isl_take isl_map *map1,
2262 __isl_take isl_map *map2);
2263 __isl_give isl_union_map *isl_union_map_apply_range(
2264 __isl_take isl_union_map *umap1,
2265 __isl_take isl_union_map *umap2);
2267 =item * Cartesian Product
2269 __isl_give isl_set *isl_set_product(
2270 __isl_take isl_set *set1,
2271 __isl_take isl_set *set2);
2272 __isl_give isl_union_set *isl_union_set_product(
2273 __isl_take isl_union_set *uset1,
2274 __isl_take isl_union_set *uset2);
2275 __isl_give isl_basic_map *isl_basic_map_domain_product(
2276 __isl_take isl_basic_map *bmap1,
2277 __isl_take isl_basic_map *bmap2);
2278 __isl_give isl_basic_map *isl_basic_map_range_product(
2279 __isl_take isl_basic_map *bmap1,
2280 __isl_take isl_basic_map *bmap2);
2281 __isl_give isl_map *isl_map_domain_product(
2282 __isl_take isl_map *map1,
2283 __isl_take isl_map *map2);
2284 __isl_give isl_map *isl_map_range_product(
2285 __isl_take isl_map *map1,
2286 __isl_take isl_map *map2);
2287 __isl_give isl_union_map *isl_union_map_range_product(
2288 __isl_take isl_union_map *umap1,
2289 __isl_take isl_union_map *umap2);
2290 __isl_give isl_map *isl_map_product(
2291 __isl_take isl_map *map1,
2292 __isl_take isl_map *map2);
2293 __isl_give isl_union_map *isl_union_map_product(
2294 __isl_take isl_union_map *umap1,
2295 __isl_take isl_union_map *umap2);
2297 The above functions compute the cross product of the given
2298 sets or relations. The domains and ranges of the results
2299 are wrapped maps between domains and ranges of the inputs.
2300 To obtain a ``flat'' product, use the following functions
2303 __isl_give isl_basic_set *isl_basic_set_flat_product(
2304 __isl_take isl_basic_set *bset1,
2305 __isl_take isl_basic_set *bset2);
2306 __isl_give isl_set *isl_set_flat_product(
2307 __isl_take isl_set *set1,
2308 __isl_take isl_set *set2);
2309 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2310 __isl_take isl_basic_map *bmap1,
2311 __isl_take isl_basic_map *bmap2);
2312 __isl_give isl_map *isl_map_flat_domain_product(
2313 __isl_take isl_map *map1,
2314 __isl_take isl_map *map2);
2315 __isl_give isl_map *isl_map_flat_range_product(
2316 __isl_take isl_map *map1,
2317 __isl_take isl_map *map2);
2318 __isl_give isl_union_map *isl_union_map_flat_range_product(
2319 __isl_take isl_union_map *umap1,
2320 __isl_take isl_union_map *umap2);
2321 __isl_give isl_basic_map *isl_basic_map_flat_product(
2322 __isl_take isl_basic_map *bmap1,
2323 __isl_take isl_basic_map *bmap2);
2324 __isl_give isl_map *isl_map_flat_product(
2325 __isl_take isl_map *map1,
2326 __isl_take isl_map *map2);
2328 =item * Simplification
2330 __isl_give isl_basic_set *isl_basic_set_gist(
2331 __isl_take isl_basic_set *bset,
2332 __isl_take isl_basic_set *context);
2333 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2334 __isl_take isl_set *context);
2335 __isl_give isl_set *isl_set_gist_params(
2336 __isl_take isl_set *set,
2337 __isl_take isl_set *context);
2338 __isl_give isl_union_set *isl_union_set_gist(
2339 __isl_take isl_union_set *uset,
2340 __isl_take isl_union_set *context);
2341 __isl_give isl_basic_map *isl_basic_map_gist(
2342 __isl_take isl_basic_map *bmap,
2343 __isl_take isl_basic_map *context);
2344 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2345 __isl_take isl_map *context);
2346 __isl_give isl_map *isl_map_gist_params(
2347 __isl_take isl_map *map,
2348 __isl_take isl_set *context);
2349 __isl_give isl_union_map *isl_union_map_gist(
2350 __isl_take isl_union_map *umap,
2351 __isl_take isl_union_map *context);
2353 The gist operation returns a set or relation that has the
2354 same intersection with the context as the input set or relation.
2355 Any implicit equality in the intersection is made explicit in the result,
2356 while all inequalities that are redundant with respect to the intersection
2358 In case of union sets and relations, the gist operation is performed
2363 =head3 Lexicographic Optimization
2365 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2366 the following functions
2367 compute a set that contains the lexicographic minimum or maximum
2368 of the elements in C<set> (or C<bset>) for those values of the parameters
2369 that satisfy C<dom>.
2370 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2371 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2373 In other words, the union of the parameter values
2374 for which the result is non-empty and of C<*empty>
2377 __isl_give isl_set *isl_basic_set_partial_lexmin(
2378 __isl_take isl_basic_set *bset,
2379 __isl_take isl_basic_set *dom,
2380 __isl_give isl_set **empty);
2381 __isl_give isl_set *isl_basic_set_partial_lexmax(
2382 __isl_take isl_basic_set *bset,
2383 __isl_take isl_basic_set *dom,
2384 __isl_give isl_set **empty);
2385 __isl_give isl_set *isl_set_partial_lexmin(
2386 __isl_take isl_set *set, __isl_take isl_set *dom,
2387 __isl_give isl_set **empty);
2388 __isl_give isl_set *isl_set_partial_lexmax(
2389 __isl_take isl_set *set, __isl_take isl_set *dom,
2390 __isl_give isl_set **empty);
2392 Given a (basic) set C<set> (or C<bset>), the following functions simply
2393 return a set containing the lexicographic minimum or maximum
2394 of the elements in C<set> (or C<bset>).
2395 In case of union sets, the optimum is computed per space.
2397 __isl_give isl_set *isl_basic_set_lexmin(
2398 __isl_take isl_basic_set *bset);
2399 __isl_give isl_set *isl_basic_set_lexmax(
2400 __isl_take isl_basic_set *bset);
2401 __isl_give isl_set *isl_set_lexmin(
2402 __isl_take isl_set *set);
2403 __isl_give isl_set *isl_set_lexmax(
2404 __isl_take isl_set *set);
2405 __isl_give isl_union_set *isl_union_set_lexmin(
2406 __isl_take isl_union_set *uset);
2407 __isl_give isl_union_set *isl_union_set_lexmax(
2408 __isl_take isl_union_set *uset);
2410 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2411 the following functions
2412 compute a relation that maps each element of C<dom>
2413 to the single lexicographic minimum or maximum
2414 of the elements that are associated to that same
2415 element in C<map> (or C<bmap>).
2416 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2417 that contains the elements in C<dom> that do not map
2418 to any elements in C<map> (or C<bmap>).
2419 In other words, the union of the domain of the result and of C<*empty>
2422 __isl_give isl_map *isl_basic_map_partial_lexmax(
2423 __isl_take isl_basic_map *bmap,
2424 __isl_take isl_basic_set *dom,
2425 __isl_give isl_set **empty);
2426 __isl_give isl_map *isl_basic_map_partial_lexmin(
2427 __isl_take isl_basic_map *bmap,
2428 __isl_take isl_basic_set *dom,
2429 __isl_give isl_set **empty);
2430 __isl_give isl_map *isl_map_partial_lexmax(
2431 __isl_take isl_map *map, __isl_take isl_set *dom,
2432 __isl_give isl_set **empty);
2433 __isl_give isl_map *isl_map_partial_lexmin(
2434 __isl_take isl_map *map, __isl_take isl_set *dom,
2435 __isl_give isl_set **empty);
2437 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2438 return a map mapping each element in the domain of
2439 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2440 of all elements associated to that element.
2441 In case of union relations, the optimum is computed per space.
2443 __isl_give isl_map *isl_basic_map_lexmin(
2444 __isl_take isl_basic_map *bmap);
2445 __isl_give isl_map *isl_basic_map_lexmax(
2446 __isl_take isl_basic_map *bmap);
2447 __isl_give isl_map *isl_map_lexmin(
2448 __isl_take isl_map *map);
2449 __isl_give isl_map *isl_map_lexmax(
2450 __isl_take isl_map *map);
2451 __isl_give isl_union_map *isl_union_map_lexmin(
2452 __isl_take isl_union_map *umap);
2453 __isl_give isl_union_map *isl_union_map_lexmax(
2454 __isl_take isl_union_map *umap);
2458 Lists are defined over several element types, including
2459 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2460 Here we take lists of C<isl_set>s as an example.
2461 Lists can be created, copied and freed using the following functions.
2463 #include <isl/list.h>
2464 __isl_give isl_set_list *isl_set_list_from_set(
2465 __isl_take isl_set *el);
2466 __isl_give isl_set_list *isl_set_list_alloc(
2467 isl_ctx *ctx, int n);
2468 __isl_give isl_set_list *isl_set_list_copy(
2469 __isl_keep isl_set_list *list);
2470 __isl_give isl_set_list *isl_set_list_add(
2471 __isl_take isl_set_list *list,
2472 __isl_take isl_set *el);
2473 __isl_give isl_set_list *isl_set_list_concat(
2474 __isl_take isl_set_list *list1,
2475 __isl_take isl_set_list *list2);
2476 void *isl_set_list_free(__isl_take isl_set_list *list);
2478 C<isl_set_list_alloc> creates an empty list with a capacity for
2479 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2482 Lists can be inspected using the following functions.
2484 #include <isl/list.h>
2485 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2486 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2487 __isl_give isl_set *isl_set_list_get_set(
2488 __isl_keep isl_set_list *list, int index);
2489 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2490 int (*fn)(__isl_take isl_set *el, void *user),
2493 Lists can be printed using
2495 #include <isl/list.h>
2496 __isl_give isl_printer *isl_printer_print_set_list(
2497 __isl_take isl_printer *p,
2498 __isl_keep isl_set_list *list);
2502 Matrices can be created, copied and freed using the following functions.
2504 #include <isl/mat.h>
2505 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2506 unsigned n_row, unsigned n_col);
2507 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2508 void isl_mat_free(__isl_take isl_mat *mat);
2510 Note that the elements of a newly created matrix may have arbitrary values.
2511 The elements can be changed and inspected using the following functions.
2513 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2514 int isl_mat_rows(__isl_keep isl_mat *mat);
2515 int isl_mat_cols(__isl_keep isl_mat *mat);
2516 int isl_mat_get_element(__isl_keep isl_mat *mat,
2517 int row, int col, isl_int *v);
2518 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2519 int row, int col, isl_int v);
2520 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2521 int row, int col, int v);
2523 C<isl_mat_get_element> will return a negative value if anything went wrong.
2524 In that case, the value of C<*v> is undefined.
2526 The following function can be used to compute the (right) inverse
2527 of a matrix, i.e., a matrix such that the product of the original
2528 and the inverse (in that order) is a multiple of the identity matrix.
2529 The input matrix is assumed to be of full row-rank.
2531 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2533 The following function can be used to compute the (right) kernel
2534 (or null space) of a matrix, i.e., a matrix such that the product of
2535 the original and the kernel (in that order) is the zero matrix.
2537 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2539 =head2 Piecewise Quasi Affine Expressions
2541 The zero quasi affine expression on a given domain can be created using
2543 __isl_give isl_aff *isl_aff_zero_on_domain(
2544 __isl_take isl_local_space *ls);
2546 Note that the space in which the resulting object lives is a map space
2547 with the given space as domain and a one-dimensional range.
2549 An empty piecewise quasi affine expression (one with no cells)
2550 or a piecewise quasi affine expression with a single cell can
2551 be created using the following functions.
2553 #include <isl/aff.h>
2554 __isl_give isl_pw_aff *isl_pw_aff_empty(
2555 __isl_take isl_space *space);
2556 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2557 __isl_take isl_set *set, __isl_take isl_aff *aff);
2558 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2559 __isl_take isl_aff *aff);
2561 Quasi affine expressions can be copied and freed using
2563 #include <isl/aff.h>
2564 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2565 void *isl_aff_free(__isl_take isl_aff *aff);
2567 __isl_give isl_pw_aff *isl_pw_aff_copy(
2568 __isl_keep isl_pw_aff *pwaff);
2569 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2571 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2572 using the following function. The constraint is required to have
2573 a non-zero coefficient for the specified dimension.
2575 #include <isl/constraint.h>
2576 __isl_give isl_aff *isl_constraint_get_bound(
2577 __isl_keep isl_constraint *constraint,
2578 enum isl_dim_type type, int pos);
2580 The entire affine expression of the constraint can also be extracted
2581 using the following function.
2583 #include <isl/constraint.h>
2584 __isl_give isl_aff *isl_constraint_get_aff(
2585 __isl_keep isl_constraint *constraint);
2587 Conversely, an equality constraint equating
2588 the affine expression to zero or an inequality constraint enforcing
2589 the affine expression to be non-negative, can be constructed using
2591 __isl_give isl_constraint *isl_equality_from_aff(
2592 __isl_take isl_aff *aff);
2593 __isl_give isl_constraint *isl_inequality_from_aff(
2594 __isl_take isl_aff *aff);
2596 The expression can be inspected using
2598 #include <isl/aff.h>
2599 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2600 int isl_aff_dim(__isl_keep isl_aff *aff,
2601 enum isl_dim_type type);
2602 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2603 __isl_keep isl_aff *aff);
2604 __isl_give isl_local_space *isl_aff_get_local_space(
2605 __isl_keep isl_aff *aff);
2606 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2607 enum isl_dim_type type, unsigned pos);
2608 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2610 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2611 enum isl_dim_type type, int pos, isl_int *v);
2612 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2614 __isl_give isl_aff *isl_aff_get_div(
2615 __isl_keep isl_aff *aff, int pos);
2617 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2618 int (*fn)(__isl_take isl_set *set,
2619 __isl_take isl_aff *aff,
2620 void *user), void *user);
2622 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2623 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2625 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2626 enum isl_dim_type type, unsigned first, unsigned n);
2627 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2628 enum isl_dim_type type, unsigned first, unsigned n);
2630 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2631 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2632 enum isl_dim_type type);
2633 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2635 It can be modified using
2637 #include <isl/aff.h>
2638 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2639 __isl_take isl_pw_aff *pwaff,
2640 enum isl_dim_type type, __isl_take isl_id *id);
2641 __isl_give isl_aff *isl_aff_set_dim_name(
2642 __isl_take isl_aff *aff, enum isl_dim_type type,
2643 unsigned pos, const char *s);
2644 __isl_give isl_aff *isl_aff_set_dim_id(
2645 __isl_take isl_aff *aff, enum isl_dim_type type,
2646 unsigned pos, __isl_take isl_id *id);
2647 __isl_give isl_aff *isl_aff_set_constant(
2648 __isl_take isl_aff *aff, isl_int v);
2649 __isl_give isl_aff *isl_aff_set_constant_si(
2650 __isl_take isl_aff *aff, int v);
2651 __isl_give isl_aff *isl_aff_set_coefficient(
2652 __isl_take isl_aff *aff,
2653 enum isl_dim_type type, int pos, isl_int v);
2654 __isl_give isl_aff *isl_aff_set_coefficient_si(
2655 __isl_take isl_aff *aff,
2656 enum isl_dim_type type, int pos, int v);
2657 __isl_give isl_aff *isl_aff_set_denominator(
2658 __isl_take isl_aff *aff, isl_int v);
2660 __isl_give isl_aff *isl_aff_add_constant(
2661 __isl_take isl_aff *aff, isl_int v);
2662 __isl_give isl_aff *isl_aff_add_constant_si(
2663 __isl_take isl_aff *aff, int v);
2664 __isl_give isl_aff *isl_aff_add_coefficient(
2665 __isl_take isl_aff *aff,
2666 enum isl_dim_type type, int pos, isl_int v);
2667 __isl_give isl_aff *isl_aff_add_coefficient_si(
2668 __isl_take isl_aff *aff,
2669 enum isl_dim_type type, int pos, int v);
2671 __isl_give isl_aff *isl_aff_insert_dims(
2672 __isl_take isl_aff *aff,
2673 enum isl_dim_type type, unsigned first, unsigned n);
2674 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2675 __isl_take isl_pw_aff *pwaff,
2676 enum isl_dim_type type, unsigned first, unsigned n);
2677 __isl_give isl_aff *isl_aff_add_dims(
2678 __isl_take isl_aff *aff,
2679 enum isl_dim_type type, unsigned n);
2680 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2681 __isl_take isl_pw_aff *pwaff,
2682 enum isl_dim_type type, unsigned n);
2683 __isl_give isl_aff *isl_aff_drop_dims(
2684 __isl_take isl_aff *aff,
2685 enum isl_dim_type type, unsigned first, unsigned n);
2686 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2687 __isl_take isl_pw_aff *pwaff,
2688 enum isl_dim_type type, unsigned first, unsigned n);
2690 Note that the C<set_constant> and C<set_coefficient> functions
2691 set the I<numerator> of the constant or coefficient, while
2692 C<add_constant> and C<add_coefficient> add an integer value to
2693 the possibly rational constant or coefficient.
2695 To check whether an affine expressions is obviously zero
2696 or obviously equal to some other affine expression, use
2698 #include <isl/aff.h>
2699 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2700 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2701 __isl_keep isl_aff *aff2);
2702 int isl_pw_aff_plain_is_equal(
2703 __isl_keep isl_pw_aff *pwaff1,
2704 __isl_keep isl_pw_aff *pwaff2);
2708 #include <isl/aff.h>
2709 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2710 __isl_take isl_aff *aff2);
2711 __isl_give isl_pw_aff *isl_pw_aff_add(
2712 __isl_take isl_pw_aff *pwaff1,
2713 __isl_take isl_pw_aff *pwaff2);
2714 __isl_give isl_pw_aff *isl_pw_aff_min(
2715 __isl_take isl_pw_aff *pwaff1,
2716 __isl_take isl_pw_aff *pwaff2);
2717 __isl_give isl_pw_aff *isl_pw_aff_max(
2718 __isl_take isl_pw_aff *pwaff1,
2719 __isl_take isl_pw_aff *pwaff2);
2720 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2721 __isl_take isl_aff *aff2);
2722 __isl_give isl_pw_aff *isl_pw_aff_sub(
2723 __isl_take isl_pw_aff *pwaff1,
2724 __isl_take isl_pw_aff *pwaff2);
2725 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2726 __isl_give isl_pw_aff *isl_pw_aff_neg(
2727 __isl_take isl_pw_aff *pwaff);
2728 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2729 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2730 __isl_take isl_pw_aff *pwaff);
2731 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2732 __isl_give isl_pw_aff *isl_pw_aff_floor(
2733 __isl_take isl_pw_aff *pwaff);
2734 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2736 __isl_give isl_pw_aff *isl_pw_aff_mod(
2737 __isl_take isl_pw_aff *pwaff, isl_int mod);
2738 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2740 __isl_give isl_pw_aff *isl_pw_aff_scale(
2741 __isl_take isl_pw_aff *pwaff, isl_int f);
2742 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2744 __isl_give isl_aff *isl_aff_scale_down_ui(
2745 __isl_take isl_aff *aff, unsigned f);
2746 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2747 __isl_take isl_pw_aff *pwaff, isl_int f);
2749 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2750 __isl_take isl_pw_aff_list *list);
2751 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2752 __isl_take isl_pw_aff_list *list);
2754 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2755 __isl_take isl_pw_aff *pwqp);
2757 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2758 __isl_take isl_pw_aff *pwaff,
2759 __isl_take isl_space *model);
2761 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2762 __isl_take isl_set *context);
2763 __isl_give isl_pw_aff *isl_pw_aff_gist(
2764 __isl_take isl_pw_aff *pwaff,
2765 __isl_take isl_set *context);
2767 __isl_give isl_set *isl_pw_aff_domain(
2768 __isl_take isl_pw_aff *pwaff);
2769 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2770 __isl_take isl_pw_aff *pa,
2771 __isl_take isl_set *set);
2773 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2774 __isl_take isl_aff *aff2);
2775 __isl_give isl_pw_aff *isl_pw_aff_mul(
2776 __isl_take isl_pw_aff *pwaff1,
2777 __isl_take isl_pw_aff *pwaff2);
2779 When multiplying two affine expressions, at least one of the two needs
2782 #include <isl/aff.h>
2783 __isl_give isl_basic_set *isl_aff_le_basic_set(
2784 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2785 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2786 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2787 __isl_give isl_set *isl_pw_aff_eq_set(
2788 __isl_take isl_pw_aff *pwaff1,
2789 __isl_take isl_pw_aff *pwaff2);
2790 __isl_give isl_set *isl_pw_aff_ne_set(
2791 __isl_take isl_pw_aff *pwaff1,
2792 __isl_take isl_pw_aff *pwaff2);
2793 __isl_give isl_set *isl_pw_aff_le_set(
2794 __isl_take isl_pw_aff *pwaff1,
2795 __isl_take isl_pw_aff *pwaff2);
2796 __isl_give isl_set *isl_pw_aff_lt_set(
2797 __isl_take isl_pw_aff *pwaff1,
2798 __isl_take isl_pw_aff *pwaff2);
2799 __isl_give isl_set *isl_pw_aff_ge_set(
2800 __isl_take isl_pw_aff *pwaff1,
2801 __isl_take isl_pw_aff *pwaff2);
2802 __isl_give isl_set *isl_pw_aff_gt_set(
2803 __isl_take isl_pw_aff *pwaff1,
2804 __isl_take isl_pw_aff *pwaff2);
2806 __isl_give isl_set *isl_pw_aff_list_eq_set(
2807 __isl_take isl_pw_aff_list *list1,
2808 __isl_take isl_pw_aff_list *list2);
2809 __isl_give isl_set *isl_pw_aff_list_ne_set(
2810 __isl_take isl_pw_aff_list *list1,
2811 __isl_take isl_pw_aff_list *list2);
2812 __isl_give isl_set *isl_pw_aff_list_le_set(
2813 __isl_take isl_pw_aff_list *list1,
2814 __isl_take isl_pw_aff_list *list2);
2815 __isl_give isl_set *isl_pw_aff_list_lt_set(
2816 __isl_take isl_pw_aff_list *list1,
2817 __isl_take isl_pw_aff_list *list2);
2818 __isl_give isl_set *isl_pw_aff_list_ge_set(
2819 __isl_take isl_pw_aff_list *list1,
2820 __isl_take isl_pw_aff_list *list2);
2821 __isl_give isl_set *isl_pw_aff_list_gt_set(
2822 __isl_take isl_pw_aff_list *list1,
2823 __isl_take isl_pw_aff_list *list2);
2825 The function C<isl_aff_ge_basic_set> returns a basic set
2826 containing those elements in the shared space
2827 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2828 The function C<isl_aff_ge_set> returns a set
2829 containing those elements in the shared domain
2830 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2831 The functions operating on C<isl_pw_aff_list> apply the corresponding
2832 C<isl_pw_aff> function to each pair of elements in the two lists.
2834 #include <isl/aff.h>
2835 __isl_give isl_set *isl_pw_aff_nonneg_set(
2836 __isl_take isl_pw_aff *pwaff);
2837 __isl_give isl_set *isl_pw_aff_zero_set(
2838 __isl_take isl_pw_aff *pwaff);
2839 __isl_give isl_set *isl_pw_aff_non_zero_set(
2840 __isl_take isl_pw_aff *pwaff);
2842 The function C<isl_pw_aff_nonneg_set> returns a set
2843 containing those elements in the domain
2844 of C<pwaff> where C<pwaff> is non-negative.
2846 #include <isl/aff.h>
2847 __isl_give isl_pw_aff *isl_pw_aff_cond(
2848 __isl_take isl_set *cond,
2849 __isl_take isl_pw_aff *pwaff_true,
2850 __isl_take isl_pw_aff *pwaff_false);
2852 The function C<isl_pw_aff_cond> performs a conditional operator
2853 and returns an expression that is equal to C<pwaff_true>
2854 for elements in C<cond> and equal to C<pwaff_false> for elements
2857 #include <isl/aff.h>
2858 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2859 __isl_take isl_pw_aff *pwaff1,
2860 __isl_take isl_pw_aff *pwaff2);
2861 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2862 __isl_take isl_pw_aff *pwaff1,
2863 __isl_take isl_pw_aff *pwaff2);
2865 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2866 expression with a domain that is the union of those of C<pwaff1> and
2867 C<pwaff2> and such that on each cell, the quasi-affine expression is
2868 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2869 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2870 associated expression is the defined one.
2872 An expression can be printed using
2874 #include <isl/aff.h>
2875 __isl_give isl_printer *isl_printer_print_aff(
2876 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2878 __isl_give isl_printer *isl_printer_print_pw_aff(
2879 __isl_take isl_printer *p,
2880 __isl_keep isl_pw_aff *pwaff);
2882 =head2 Multiple Quasi Affine Expressions
2884 An C<isl_multi_aff> object represents a sequence of
2885 zero or more affine expressions, all defined on the same domain space.
2887 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
2890 #include <isl/aff.h>
2891 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2892 __isl_take isl_space *space,
2893 __isl_take isl_aff_list *list);
2895 Multiple quasi affine expressions can be copied and freed using
2897 #include <isl/aff.h>
2898 __isl_give isl_multi_aff *isl_multi_aff_copy(
2899 __isl_keep isl_multi_aff *maff);
2900 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
2902 The expression can be inspected using
2904 #include <isl/aff.h>
2905 isl_ctx *isl_multi_aff_get_ctx(
2906 __isl_keep isl_multi_aff *maff);
2907 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
2908 enum isl_dim_type type);
2909 __isl_give isl_aff *isl_multi_aff_get_aff(
2910 __isl_keep isl_multi_aff *multi, int pos);
2911 const char *isl_multi_aff_get_tuple_name(
2912 __isl_keep isl_multi_aff *multi,
2913 enum isl_dim_type type);
2915 It can be modified using
2917 #include <isl/aff.h>
2918 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
2919 __isl_take isl_multi_aff *maff,
2920 enum isl_dim_type type, unsigned pos, const char *s);
2922 To check whether two multiple affine expressions are
2923 obviously equal to each other, use
2925 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
2926 __isl_keep isl_multi_aff *maff2);
2930 #include <isl/aff.h>
2931 __isl_give isl_multi_aff *isl_multi_aff_add(
2932 __isl_take isl_multi_aff *maff1,
2933 __isl_take isl_multi_aff *maff2);
2934 __isl_give isl_multi_aff *isl_multi_aff_scale(
2935 __isl_take isl_multi_aff *maff,
2937 __isl_give isl_multi_aff *isl_multi_aff_gist(
2938 __isl_take isl_multi_aff *maff,
2939 __isl_take isl_set *context);
2941 An expression can be printed using
2943 #include <isl/aff.h>
2944 __isl_give isl_printer *isl_printer_print_multi_aff(
2945 __isl_take isl_printer *p,
2946 __isl_keep isl_multi_aff *maff);
2950 Points are elements of a set. They can be used to construct
2951 simple sets (boxes) or they can be used to represent the
2952 individual elements of a set.
2953 The zero point (the origin) can be created using
2955 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2957 The coordinates of a point can be inspected, set and changed
2960 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2961 enum isl_dim_type type, int pos, isl_int *v);
2962 __isl_give isl_point *isl_point_set_coordinate(
2963 __isl_take isl_point *pnt,
2964 enum isl_dim_type type, int pos, isl_int v);
2966 __isl_give isl_point *isl_point_add_ui(
2967 __isl_take isl_point *pnt,
2968 enum isl_dim_type type, int pos, unsigned val);
2969 __isl_give isl_point *isl_point_sub_ui(
2970 __isl_take isl_point *pnt,
2971 enum isl_dim_type type, int pos, unsigned val);
2973 Other properties can be obtained using
2975 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2977 Points can be copied or freed using
2979 __isl_give isl_point *isl_point_copy(
2980 __isl_keep isl_point *pnt);
2981 void isl_point_free(__isl_take isl_point *pnt);
2983 A singleton set can be created from a point using
2985 __isl_give isl_basic_set *isl_basic_set_from_point(
2986 __isl_take isl_point *pnt);
2987 __isl_give isl_set *isl_set_from_point(
2988 __isl_take isl_point *pnt);
2990 and a box can be created from two opposite extremal points using
2992 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2993 __isl_take isl_point *pnt1,
2994 __isl_take isl_point *pnt2);
2995 __isl_give isl_set *isl_set_box_from_points(
2996 __isl_take isl_point *pnt1,
2997 __isl_take isl_point *pnt2);
2999 All elements of a B<bounded> (union) set can be enumerated using
3000 the following functions.
3002 int isl_set_foreach_point(__isl_keep isl_set *set,
3003 int (*fn)(__isl_take isl_point *pnt, void *user),
3005 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3006 int (*fn)(__isl_take isl_point *pnt, void *user),
3009 The function C<fn> is called for each integer point in
3010 C<set> with as second argument the last argument of
3011 the C<isl_set_foreach_point> call. The function C<fn>
3012 should return C<0> on success and C<-1> on failure.
3013 In the latter case, C<isl_set_foreach_point> will stop
3014 enumerating and return C<-1> as well.
3015 If the enumeration is performed successfully and to completion,
3016 then C<isl_set_foreach_point> returns C<0>.
3018 To obtain a single point of a (basic) set, use
3020 __isl_give isl_point *isl_basic_set_sample_point(
3021 __isl_take isl_basic_set *bset);
3022 __isl_give isl_point *isl_set_sample_point(
3023 __isl_take isl_set *set);
3025 If C<set> does not contain any (integer) points, then the
3026 resulting point will be ``void'', a property that can be
3029 int isl_point_is_void(__isl_keep isl_point *pnt);
3031 =head2 Piecewise Quasipolynomials
3033 A piecewise quasipolynomial is a particular kind of function that maps
3034 a parametric point to a rational value.
3035 More specifically, a quasipolynomial is a polynomial expression in greatest
3036 integer parts of affine expressions of parameters and variables.
3037 A piecewise quasipolynomial is a subdivision of a given parametric
3038 domain into disjoint cells with a quasipolynomial associated to
3039 each cell. The value of the piecewise quasipolynomial at a given
3040 point is the value of the quasipolynomial associated to the cell
3041 that contains the point. Outside of the union of cells,
3042 the value is assumed to be zero.
3043 For example, the piecewise quasipolynomial
3045 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3047 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3048 A given piecewise quasipolynomial has a fixed domain dimension.
3049 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3050 defined over different domains.
3051 Piecewise quasipolynomials are mainly used by the C<barvinok>
3052 library for representing the number of elements in a parametric set or map.
3053 For example, the piecewise quasipolynomial above represents
3054 the number of points in the map
3056 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3058 =head3 Printing (Piecewise) Quasipolynomials
3060 Quasipolynomials and piecewise quasipolynomials can be printed
3061 using the following functions.
3063 __isl_give isl_printer *isl_printer_print_qpolynomial(
3064 __isl_take isl_printer *p,
3065 __isl_keep isl_qpolynomial *qp);
3067 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3068 __isl_take isl_printer *p,
3069 __isl_keep isl_pw_qpolynomial *pwqp);
3071 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3072 __isl_take isl_printer *p,
3073 __isl_keep isl_union_pw_qpolynomial *upwqp);
3075 The output format of the printer
3076 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3077 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3079 In case of printing in C<ISL_FORMAT_C>, the user may want
3080 to set the names of all dimensions
3082 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3083 __isl_take isl_qpolynomial *qp,
3084 enum isl_dim_type type, unsigned pos,
3086 __isl_give isl_pw_qpolynomial *
3087 isl_pw_qpolynomial_set_dim_name(
3088 __isl_take isl_pw_qpolynomial *pwqp,
3089 enum isl_dim_type type, unsigned pos,
3092 =head3 Creating New (Piecewise) Quasipolynomials
3094 Some simple quasipolynomials can be created using the following functions.
3095 More complicated quasipolynomials can be created by applying
3096 operations such as addition and multiplication
3097 on the resulting quasipolynomials
3099 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3100 __isl_take isl_space *domain);
3101 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3102 __isl_take isl_space *domain);
3103 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3104 __isl_take isl_space *domain);
3105 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3106 __isl_take isl_space *domain);
3107 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3108 __isl_take isl_space *domain);
3109 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3110 __isl_take isl_space *domain,
3111 const isl_int n, const isl_int d);
3112 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3113 __isl_take isl_space *domain,
3114 enum isl_dim_type type, unsigned pos);
3115 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3116 __isl_take isl_aff *aff);
3118 Note that the space in which a quasipolynomial lives is a map space
3119 with a one-dimensional range. The C<domain> argument in some of
3120 the functions above corresponds to the domain of this map space.
3122 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3123 with a single cell can be created using the following functions.
3124 Multiple of these single cell piecewise quasipolynomials can
3125 be combined to create more complicated piecewise quasipolynomials.
3127 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3128 __isl_take isl_space *space);
3129 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3130 __isl_take isl_set *set,
3131 __isl_take isl_qpolynomial *qp);
3132 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3133 __isl_take isl_qpolynomial *qp);
3134 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3135 __isl_take isl_pw_aff *pwaff);
3137 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3138 __isl_take isl_space *space);
3139 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3140 __isl_take isl_pw_qpolynomial *pwqp);
3141 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3142 __isl_take isl_union_pw_qpolynomial *upwqp,
3143 __isl_take isl_pw_qpolynomial *pwqp);
3145 Quasipolynomials can be copied and freed again using the following
3148 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3149 __isl_keep isl_qpolynomial *qp);
3150 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3152 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3153 __isl_keep isl_pw_qpolynomial *pwqp);
3154 void *isl_pw_qpolynomial_free(
3155 __isl_take isl_pw_qpolynomial *pwqp);
3157 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3158 __isl_keep isl_union_pw_qpolynomial *upwqp);
3159 void isl_union_pw_qpolynomial_free(
3160 __isl_take isl_union_pw_qpolynomial *upwqp);
3162 =head3 Inspecting (Piecewise) Quasipolynomials
3164 To iterate over all piecewise quasipolynomials in a union
3165 piecewise quasipolynomial, use the following function
3167 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3168 __isl_keep isl_union_pw_qpolynomial *upwqp,
3169 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3172 To extract the piecewise quasipolynomial in a given space from a union, use
3174 __isl_give isl_pw_qpolynomial *
3175 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3176 __isl_keep isl_union_pw_qpolynomial *upwqp,
3177 __isl_take isl_space *space);
3179 To iterate over the cells in a piecewise quasipolynomial,
3180 use either of the following two functions
3182 int isl_pw_qpolynomial_foreach_piece(
3183 __isl_keep isl_pw_qpolynomial *pwqp,
3184 int (*fn)(__isl_take isl_set *set,
3185 __isl_take isl_qpolynomial *qp,
3186 void *user), void *user);
3187 int isl_pw_qpolynomial_foreach_lifted_piece(
3188 __isl_keep isl_pw_qpolynomial *pwqp,
3189 int (*fn)(__isl_take isl_set *set,
3190 __isl_take isl_qpolynomial *qp,
3191 void *user), void *user);
3193 As usual, the function C<fn> should return C<0> on success
3194 and C<-1> on failure. The difference between
3195 C<isl_pw_qpolynomial_foreach_piece> and
3196 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3197 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3198 compute unique representations for all existentially quantified
3199 variables and then turn these existentially quantified variables
3200 into extra set variables, adapting the associated quasipolynomial
3201 accordingly. This means that the C<set> passed to C<fn>
3202 will not have any existentially quantified variables, but that
3203 the dimensions of the sets may be different for different
3204 invocations of C<fn>.
3206 To iterate over all terms in a quasipolynomial,
3209 int isl_qpolynomial_foreach_term(
3210 __isl_keep isl_qpolynomial *qp,
3211 int (*fn)(__isl_take isl_term *term,
3212 void *user), void *user);
3214 The terms themselves can be inspected and freed using
3217 unsigned isl_term_dim(__isl_keep isl_term *term,
3218 enum isl_dim_type type);
3219 void isl_term_get_num(__isl_keep isl_term *term,
3221 void isl_term_get_den(__isl_keep isl_term *term,
3223 int isl_term_get_exp(__isl_keep isl_term *term,
3224 enum isl_dim_type type, unsigned pos);
3225 __isl_give isl_aff *isl_term_get_div(
3226 __isl_keep isl_term *term, unsigned pos);
3227 void isl_term_free(__isl_take isl_term *term);
3229 Each term is a product of parameters, set variables and
3230 integer divisions. The function C<isl_term_get_exp>
3231 returns the exponent of a given dimensions in the given term.
3232 The C<isl_int>s in the arguments of C<isl_term_get_num>
3233 and C<isl_term_get_den> need to have been initialized
3234 using C<isl_int_init> before calling these functions.
3236 =head3 Properties of (Piecewise) Quasipolynomials
3238 To check whether a quasipolynomial is actually a constant,
3239 use the following function.
3241 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3242 isl_int *n, isl_int *d);
3244 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3245 then the numerator and denominator of the constant
3246 are returned in C<*n> and C<*d>, respectively.
3248 To check whether two union piecewise quasipolynomials are
3249 obviously equal, use
3251 int isl_union_pw_qpolynomial_plain_is_equal(
3252 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3253 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3255 =head3 Operations on (Piecewise) Quasipolynomials
3257 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3258 __isl_take isl_qpolynomial *qp, isl_int v);
3259 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3260 __isl_take isl_qpolynomial *qp);
3261 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3262 __isl_take isl_qpolynomial *qp1,
3263 __isl_take isl_qpolynomial *qp2);
3264 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3265 __isl_take isl_qpolynomial *qp1,
3266 __isl_take isl_qpolynomial *qp2);
3267 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3268 __isl_take isl_qpolynomial *qp1,
3269 __isl_take isl_qpolynomial *qp2);
3270 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3271 __isl_take isl_qpolynomial *qp, unsigned exponent);
3273 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3274 __isl_take isl_pw_qpolynomial *pwqp1,
3275 __isl_take isl_pw_qpolynomial *pwqp2);
3276 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3277 __isl_take isl_pw_qpolynomial *pwqp1,
3278 __isl_take isl_pw_qpolynomial *pwqp2);
3279 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3280 __isl_take isl_pw_qpolynomial *pwqp1,
3281 __isl_take isl_pw_qpolynomial *pwqp2);
3282 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3283 __isl_take isl_pw_qpolynomial *pwqp);
3284 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3285 __isl_take isl_pw_qpolynomial *pwqp1,
3286 __isl_take isl_pw_qpolynomial *pwqp2);
3287 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3288 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3290 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3291 __isl_take isl_union_pw_qpolynomial *upwqp1,
3292 __isl_take isl_union_pw_qpolynomial *upwqp2);
3293 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3294 __isl_take isl_union_pw_qpolynomial *upwqp1,
3295 __isl_take isl_union_pw_qpolynomial *upwqp2);
3296 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3297 __isl_take isl_union_pw_qpolynomial *upwqp1,
3298 __isl_take isl_union_pw_qpolynomial *upwqp2);
3300 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3301 __isl_take isl_pw_qpolynomial *pwqp,
3302 __isl_take isl_point *pnt);
3304 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3305 __isl_take isl_union_pw_qpolynomial *upwqp,
3306 __isl_take isl_point *pnt);
3308 __isl_give isl_set *isl_pw_qpolynomial_domain(
3309 __isl_take isl_pw_qpolynomial *pwqp);
3310 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3311 __isl_take isl_pw_qpolynomial *pwpq,
3312 __isl_take isl_set *set);
3314 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3315 __isl_take isl_union_pw_qpolynomial *upwqp);
3316 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3317 __isl_take isl_union_pw_qpolynomial *upwpq,
3318 __isl_take isl_union_set *uset);
3320 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3321 __isl_take isl_qpolynomial *qp,
3322 __isl_take isl_space *model);
3324 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3325 __isl_take isl_qpolynomial *qp);
3326 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3327 __isl_take isl_pw_qpolynomial *pwqp);
3329 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3330 __isl_take isl_union_pw_qpolynomial *upwqp);
3332 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3333 __isl_take isl_qpolynomial *qp,
3334 __isl_take isl_set *context);
3336 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3337 __isl_take isl_pw_qpolynomial *pwqp,
3338 __isl_take isl_set *context);
3340 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3341 __isl_take isl_union_pw_qpolynomial *upwqp,
3342 __isl_take isl_union_set *context);
3344 The gist operation applies the gist operation to each of
3345 the cells in the domain of the input piecewise quasipolynomial.
3346 The context is also exploited
3347 to simplify the quasipolynomials associated to each cell.
3349 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3350 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3351 __isl_give isl_union_pw_qpolynomial *
3352 isl_union_pw_qpolynomial_to_polynomial(
3353 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3355 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3356 the polynomial will be an overapproximation. If C<sign> is negative,
3357 it will be an underapproximation. If C<sign> is zero, the approximation
3358 will lie somewhere in between.
3360 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3362 A piecewise quasipolynomial reduction is a piecewise
3363 reduction (or fold) of quasipolynomials.
3364 In particular, the reduction can be maximum or a minimum.
3365 The objects are mainly used to represent the result of
3366 an upper or lower bound on a quasipolynomial over its domain,
3367 i.e., as the result of the following function.
3369 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3370 __isl_take isl_pw_qpolynomial *pwqp,
3371 enum isl_fold type, int *tight);
3373 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3374 __isl_take isl_union_pw_qpolynomial *upwqp,
3375 enum isl_fold type, int *tight);
3377 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3378 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3379 is the returned bound is known be tight, i.e., for each value
3380 of the parameters there is at least
3381 one element in the domain that reaches the bound.
3382 If the domain of C<pwqp> is not wrapping, then the bound is computed
3383 over all elements in that domain and the result has a purely parametric
3384 domain. If the domain of C<pwqp> is wrapping, then the bound is
3385 computed over the range of the wrapped relation. The domain of the
3386 wrapped relation becomes the domain of the result.
3388 A (piecewise) quasipolynomial reduction can be copied or freed using the
3389 following functions.
3391 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3392 __isl_keep isl_qpolynomial_fold *fold);
3393 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3394 __isl_keep isl_pw_qpolynomial_fold *pwf);
3395 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3396 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3397 void isl_qpolynomial_fold_free(
3398 __isl_take isl_qpolynomial_fold *fold);
3399 void *isl_pw_qpolynomial_fold_free(
3400 __isl_take isl_pw_qpolynomial_fold *pwf);
3401 void isl_union_pw_qpolynomial_fold_free(
3402 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3404 =head3 Printing Piecewise Quasipolynomial Reductions
3406 Piecewise quasipolynomial reductions can be printed
3407 using the following function.
3409 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3410 __isl_take isl_printer *p,
3411 __isl_keep isl_pw_qpolynomial_fold *pwf);
3412 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3413 __isl_take isl_printer *p,
3414 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3416 For C<isl_printer_print_pw_qpolynomial_fold>,
3417 output format of the printer
3418 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3419 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3420 output format of the printer
3421 needs to be set to C<ISL_FORMAT_ISL>.
3422 In case of printing in C<ISL_FORMAT_C>, the user may want
3423 to set the names of all dimensions
3425 __isl_give isl_pw_qpolynomial_fold *
3426 isl_pw_qpolynomial_fold_set_dim_name(
3427 __isl_take isl_pw_qpolynomial_fold *pwf,
3428 enum isl_dim_type type, unsigned pos,
3431 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3433 To iterate over all piecewise quasipolynomial reductions in a union
3434 piecewise quasipolynomial reduction, use the following function
3436 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3437 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3438 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3439 void *user), void *user);
3441 To iterate over the cells in a piecewise quasipolynomial reduction,
3442 use either of the following two functions
3444 int isl_pw_qpolynomial_fold_foreach_piece(
3445 __isl_keep isl_pw_qpolynomial_fold *pwf,
3446 int (*fn)(__isl_take isl_set *set,
3447 __isl_take isl_qpolynomial_fold *fold,
3448 void *user), void *user);
3449 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3450 __isl_keep isl_pw_qpolynomial_fold *pwf,
3451 int (*fn)(__isl_take isl_set *set,
3452 __isl_take isl_qpolynomial_fold *fold,
3453 void *user), void *user);
3455 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3456 of the difference between these two functions.
3458 To iterate over all quasipolynomials in a reduction, use
3460 int isl_qpolynomial_fold_foreach_qpolynomial(
3461 __isl_keep isl_qpolynomial_fold *fold,
3462 int (*fn)(__isl_take isl_qpolynomial *qp,
3463 void *user), void *user);
3465 =head3 Properties of Piecewise Quasipolynomial Reductions
3467 To check whether two union piecewise quasipolynomial reductions are
3468 obviously equal, use
3470 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3471 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3472 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3474 =head3 Operations on Piecewise Quasipolynomial Reductions
3476 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3477 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3479 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3480 __isl_take isl_pw_qpolynomial_fold *pwf1,
3481 __isl_take isl_pw_qpolynomial_fold *pwf2);
3483 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3484 __isl_take isl_pw_qpolynomial_fold *pwf1,
3485 __isl_take isl_pw_qpolynomial_fold *pwf2);
3487 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3488 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3489 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3491 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3492 __isl_take isl_pw_qpolynomial_fold *pwf,
3493 __isl_take isl_point *pnt);
3495 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3496 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3497 __isl_take isl_point *pnt);
3499 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3500 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3501 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3502 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3503 __isl_take isl_union_set *uset);
3505 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3506 __isl_take isl_pw_qpolynomial_fold *pwf);
3508 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3509 __isl_take isl_pw_qpolynomial_fold *pwf);
3511 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3512 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3514 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3515 __isl_take isl_pw_qpolynomial_fold *pwf,
3516 __isl_take isl_set *context);
3518 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3519 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3520 __isl_take isl_union_set *context);
3522 The gist operation applies the gist operation to each of
3523 the cells in the domain of the input piecewise quasipolynomial reduction.
3524 In future, the operation will also exploit the context
3525 to simplify the quasipolynomial reductions associated to each cell.
3527 __isl_give isl_pw_qpolynomial_fold *
3528 isl_set_apply_pw_qpolynomial_fold(
3529 __isl_take isl_set *set,
3530 __isl_take isl_pw_qpolynomial_fold *pwf,
3532 __isl_give isl_pw_qpolynomial_fold *
3533 isl_map_apply_pw_qpolynomial_fold(
3534 __isl_take isl_map *map,
3535 __isl_take isl_pw_qpolynomial_fold *pwf,
3537 __isl_give isl_union_pw_qpolynomial_fold *
3538 isl_union_set_apply_union_pw_qpolynomial_fold(
3539 __isl_take isl_union_set *uset,
3540 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3542 __isl_give isl_union_pw_qpolynomial_fold *
3543 isl_union_map_apply_union_pw_qpolynomial_fold(
3544 __isl_take isl_union_map *umap,
3545 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3548 The functions taking a map
3549 compose the given map with the given piecewise quasipolynomial reduction.
3550 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3551 over all elements in the intersection of the range of the map
3552 and the domain of the piecewise quasipolynomial reduction
3553 as a function of an element in the domain of the map.
3554 The functions taking a set compute a bound over all elements in the
3555 intersection of the set and the domain of the
3556 piecewise quasipolynomial reduction.
3558 =head2 Dependence Analysis
3560 C<isl> contains specialized functionality for performing
3561 array dataflow analysis. That is, given a I<sink> access relation
3562 and a collection of possible I<source> access relations,
3563 C<isl> can compute relations that describe
3564 for each iteration of the sink access, which iteration
3565 of which of the source access relations was the last
3566 to access the same data element before the given iteration
3568 To compute standard flow dependences, the sink should be
3569 a read, while the sources should be writes.
3570 If any of the source accesses are marked as being I<may>
3571 accesses, then there will be a dependence to the last
3572 I<must> access B<and> to any I<may> access that follows
3573 this last I<must> access.
3574 In particular, if I<all> sources are I<may> accesses,
3575 then memory based dependence analysis is performed.
3576 If, on the other hand, all sources are I<must> accesses,
3577 then value based dependence analysis is performed.
3579 #include <isl/flow.h>
3581 typedef int (*isl_access_level_before)(void *first, void *second);
3583 __isl_give isl_access_info *isl_access_info_alloc(
3584 __isl_take isl_map *sink,
3585 void *sink_user, isl_access_level_before fn,
3587 __isl_give isl_access_info *isl_access_info_add_source(
3588 __isl_take isl_access_info *acc,
3589 __isl_take isl_map *source, int must,
3591 void isl_access_info_free(__isl_take isl_access_info *acc);
3593 __isl_give isl_flow *isl_access_info_compute_flow(
3594 __isl_take isl_access_info *acc);
3596 int isl_flow_foreach(__isl_keep isl_flow *deps,
3597 int (*fn)(__isl_take isl_map *dep, int must,
3598 void *dep_user, void *user),
3600 __isl_give isl_map *isl_flow_get_no_source(
3601 __isl_keep isl_flow *deps, int must);
3602 void isl_flow_free(__isl_take isl_flow *deps);
3604 The function C<isl_access_info_compute_flow> performs the actual
3605 dependence analysis. The other functions are used to construct
3606 the input for this function or to read off the output.
3608 The input is collected in an C<isl_access_info>, which can
3609 be created through a call to C<isl_access_info_alloc>.
3610 The arguments to this functions are the sink access relation
3611 C<sink>, a token C<sink_user> used to identify the sink
3612 access to the user, a callback function for specifying the
3613 relative order of source and sink accesses, and the number
3614 of source access relations that will be added.
3615 The callback function has type C<int (*)(void *first, void *second)>.
3616 The function is called with two user supplied tokens identifying
3617 either a source or the sink and it should return the shared nesting
3618 level and the relative order of the two accesses.
3619 In particular, let I<n> be the number of loops shared by
3620 the two accesses. If C<first> precedes C<second> textually,
3621 then the function should return I<2 * n + 1>; otherwise,
3622 it should return I<2 * n>.
3623 The sources can be added to the C<isl_access_info> by performing
3624 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3625 C<must> indicates whether the source is a I<must> access
3626 or a I<may> access. Note that a multi-valued access relation
3627 should only be marked I<must> if every iteration in the domain
3628 of the relation accesses I<all> elements in its image.
3629 The C<source_user> token is again used to identify
3630 the source access. The range of the source access relation
3631 C<source> should have the same dimension as the range
3632 of the sink access relation.
3633 The C<isl_access_info_free> function should usually not be
3634 called explicitly, because it is called implicitly by
3635 C<isl_access_info_compute_flow>.
3637 The result of the dependence analysis is collected in an
3638 C<isl_flow>. There may be elements of
3639 the sink access for which no preceding source access could be
3640 found or for which all preceding sources are I<may> accesses.
3641 The relations containing these elements can be obtained through
3642 calls to C<isl_flow_get_no_source>, the first with C<must> set
3643 and the second with C<must> unset.
3644 In the case of standard flow dependence analysis,
3645 with the sink a read and the sources I<must> writes,
3646 the first relation corresponds to the reads from uninitialized
3647 array elements and the second relation is empty.
3648 The actual flow dependences can be extracted using
3649 C<isl_flow_foreach>. This function will call the user-specified
3650 callback function C<fn> for each B<non-empty> dependence between
3651 a source and the sink. The callback function is called
3652 with four arguments, the actual flow dependence relation
3653 mapping source iterations to sink iterations, a boolean that
3654 indicates whether it is a I<must> or I<may> dependence, a token
3655 identifying the source and an additional C<void *> with value
3656 equal to the third argument of the C<isl_flow_foreach> call.
3657 A dependence is marked I<must> if it originates from a I<must>
3658 source and if it is not followed by any I<may> sources.
3660 After finishing with an C<isl_flow>, the user should call
3661 C<isl_flow_free> to free all associated memory.
3663 A higher-level interface to dependence analysis is provided
3664 by the following function.
3666 #include <isl/flow.h>
3668 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3669 __isl_take isl_union_map *must_source,
3670 __isl_take isl_union_map *may_source,
3671 __isl_take isl_union_map *schedule,
3672 __isl_give isl_union_map **must_dep,
3673 __isl_give isl_union_map **may_dep,
3674 __isl_give isl_union_map **must_no_source,
3675 __isl_give isl_union_map **may_no_source);
3677 The arrays are identified by the tuple names of the ranges
3678 of the accesses. The iteration domains by the tuple names
3679 of the domains of the accesses and of the schedule.
3680 The relative order of the iteration domains is given by the
3681 schedule. The relations returned through C<must_no_source>
3682 and C<may_no_source> are subsets of C<sink>.
3683 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3684 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3685 any of the other arguments is treated as an error.
3689 B<The functionality described in this section is fairly new
3690 and may be subject to change.>
3692 The following function can be used to compute a schedule
3693 for a union of domains. The generated schedule respects
3694 all C<validity> dependences. That is, all dependence distances
3695 over these dependences in the scheduled space are lexicographically
3696 positive. The generated schedule schedule also tries to minimize
3697 the dependence distances over C<proximity> dependences.
3698 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3699 for groups of domains where the dependence distances have only
3700 non-negative values.
3701 The algorithm used to construct the schedule is similar to that
3704 #include <isl/schedule.h>
3705 __isl_give isl_schedule *isl_union_set_compute_schedule(
3706 __isl_take isl_union_set *domain,
3707 __isl_take isl_union_map *validity,
3708 __isl_take isl_union_map *proximity);
3709 void *isl_schedule_free(__isl_take isl_schedule *sched);
3711 A mapping from the domains to the scheduled space can be obtained
3712 from an C<isl_schedule> using the following function.
3714 __isl_give isl_union_map *isl_schedule_get_map(
3715 __isl_keep isl_schedule *sched);
3717 A representation of the schedule can be printed using
3719 __isl_give isl_printer *isl_printer_print_schedule(
3720 __isl_take isl_printer *p,
3721 __isl_keep isl_schedule *schedule);
3723 A representation of the schedule as a forest of bands can be obtained
3724 using the following function.
3726 __isl_give isl_band_list *isl_schedule_get_band_forest(
3727 __isl_keep isl_schedule *schedule);
3729 The list can be manipulated as explained in L<"Lists">.
3730 The bands inside the list can be copied and freed using the following
3733 #include <isl/band.h>
3734 __isl_give isl_band *isl_band_copy(
3735 __isl_keep isl_band *band);
3736 void *isl_band_free(__isl_take isl_band *band);
3738 Each band contains zero or more scheduling dimensions.
3739 These are referred to as the members of the band.
3740 The section of the schedule that corresponds to the band is
3741 referred to as the partial schedule of the band.
3742 For those nodes that participate in a band, the outer scheduling
3743 dimensions form the prefix schedule, while the inner scheduling
3744 dimensions form the suffix schedule.
3745 That is, if we take a cut of the band forest, then the union of
3746 the concatenations of the prefix, partial and suffix schedules of
3747 each band in the cut is equal to the entire schedule (modulo
3748 some possible padding at the end with zero scheduling dimensions).
3749 The properties of a band can be inspected using the following functions.
3751 #include <isl/band.h>
3752 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3754 int isl_band_has_children(__isl_keep isl_band *band);
3755 __isl_give isl_band_list *isl_band_get_children(
3756 __isl_keep isl_band *band);
3758 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3759 __isl_keep isl_band *band);
3760 __isl_give isl_union_map *isl_band_get_partial_schedule(
3761 __isl_keep isl_band *band);
3762 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3763 __isl_keep isl_band *band);
3765 int isl_band_n_member(__isl_keep isl_band *band);
3766 int isl_band_member_is_zero_distance(
3767 __isl_keep isl_band *band, int pos);
3769 Note that a scheduling dimension is considered to be ``zero
3770 distance'' if it does not carry any proximity dependences
3772 That is, if the dependence distances of the proximity
3773 dependences are all zero in that direction (for fixed
3774 iterations of outer bands).
3776 A representation of the band can be printed using
3778 #include <isl/band.h>
3779 __isl_give isl_printer *isl_printer_print_band(
3780 __isl_take isl_printer *p,
3781 __isl_keep isl_band *band);
3783 =head2 Parametric Vertex Enumeration
3785 The parametric vertex enumeration described in this section
3786 is mainly intended to be used internally and by the C<barvinok>
3789 #include <isl/vertices.h>
3790 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3791 __isl_keep isl_basic_set *bset);
3793 The function C<isl_basic_set_compute_vertices> performs the
3794 actual computation of the parametric vertices and the chamber
3795 decomposition and store the result in an C<isl_vertices> object.
3796 This information can be queried by either iterating over all
3797 the vertices or iterating over all the chambers or cells
3798 and then iterating over all vertices that are active on the chamber.
3800 int isl_vertices_foreach_vertex(
3801 __isl_keep isl_vertices *vertices,
3802 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3805 int isl_vertices_foreach_cell(
3806 __isl_keep isl_vertices *vertices,
3807 int (*fn)(__isl_take isl_cell *cell, void *user),
3809 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3810 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3813 Other operations that can be performed on an C<isl_vertices> object are
3816 isl_ctx *isl_vertices_get_ctx(
3817 __isl_keep isl_vertices *vertices);
3818 int isl_vertices_get_n_vertices(
3819 __isl_keep isl_vertices *vertices);
3820 void isl_vertices_free(__isl_take isl_vertices *vertices);
3822 Vertices can be inspected and destroyed using the following functions.
3824 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3825 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3826 __isl_give isl_basic_set *isl_vertex_get_domain(
3827 __isl_keep isl_vertex *vertex);
3828 __isl_give isl_basic_set *isl_vertex_get_expr(
3829 __isl_keep isl_vertex *vertex);
3830 void isl_vertex_free(__isl_take isl_vertex *vertex);
3832 C<isl_vertex_get_expr> returns a singleton parametric set describing
3833 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3835 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3836 B<rational> basic sets, so they should mainly be used for inspection
3837 and should not be mixed with integer sets.
3839 Chambers can be inspected and destroyed using the following functions.
3841 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3842 __isl_give isl_basic_set *isl_cell_get_domain(
3843 __isl_keep isl_cell *cell);
3844 void isl_cell_free(__isl_take isl_cell *cell);
3848 Although C<isl> is mainly meant to be used as a library,
3849 it also contains some basic applications that use some
3850 of the functionality of C<isl>.
3851 The input may be specified in either the L<isl format>
3852 or the L<PolyLib format>.
3854 =head2 C<isl_polyhedron_sample>
3856 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3857 an integer element of the polyhedron, if there is any.
3858 The first column in the output is the denominator and is always
3859 equal to 1. If the polyhedron contains no integer points,
3860 then a vector of length zero is printed.
3864 C<isl_pip> takes the same input as the C<example> program
3865 from the C<piplib> distribution, i.e., a set of constraints
3866 on the parameters, a line containing only -1 and finally a set
3867 of constraints on a parametric polyhedron.
3868 The coefficients of the parameters appear in the last columns
3869 (but before the final constant column).
3870 The output is the lexicographic minimum of the parametric polyhedron.
3871 As C<isl> currently does not have its own output format, the output
3872 is just a dump of the internal state.
3874 =head2 C<isl_polyhedron_minimize>
3876 C<isl_polyhedron_minimize> computes the minimum of some linear
3877 or affine objective function over the integer points in a polyhedron.
3878 If an affine objective function
3879 is given, then the constant should appear in the last column.
3881 =head2 C<isl_polytope_scan>
3883 Given a polytope, C<isl_polytope_scan> prints
3884 all integer points in the polytope.