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 the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
90 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
91 Some of the old names have been kept for backward compatibility,
92 but they will be removed in the future.
96 =head3 Changes since isl-0.07
100 =item * The function C<isl_pw_aff_max> has been renamed to
101 C<isl_pw_aff_union_max>.
107 The source of C<isl> can be obtained either as a tarball
108 or from the git repository. Both are available from
109 L<http://freshmeat.net/projects/isl/>.
110 The installation process depends on how you obtained
113 =head2 Installation from the git repository
117 =item 1 Clone or update the repository
119 The first time the source is obtained, you need to clone
122 git clone git://repo.or.cz/isl.git
124 To obtain updates, you need to pull in the latest changes
128 =item 2 Generate C<configure>
134 After performing the above steps, continue
135 with the L<Common installation instructions>.
137 =head2 Common installation instructions
141 =item 1 Obtain C<GMP>
143 Building C<isl> requires C<GMP>, including its headers files.
144 Your distribution may not provide these header files by default
145 and you may need to install a package called C<gmp-devel> or something
146 similar. Alternatively, C<GMP> can be built from
147 source, available from L<http://gmplib.org/>.
151 C<isl> uses the standard C<autoconf> C<configure> script.
156 optionally followed by some configure options.
157 A complete list of options can be obtained by running
161 Below we discuss some of the more common options.
163 C<isl> can optionally use C<piplib>, but no
164 C<piplib> functionality is currently used by default.
165 The C<--with-piplib> option can
166 be used to specify which C<piplib>
167 library to use, either an installed version (C<system>),
168 an externally built version (C<build>)
169 or no version (C<no>). The option C<build> is mostly useful
170 in C<configure> scripts of larger projects that bundle both C<isl>
177 Installation prefix for C<isl>
179 =item C<--with-gmp-prefix>
181 Installation prefix for C<GMP> (architecture-independent files).
183 =item C<--with-gmp-exec-prefix>
185 Installation prefix for C<GMP> (architecture-dependent files).
187 =item C<--with-piplib>
189 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
191 =item C<--with-piplib-prefix>
193 Installation prefix for C<system> C<piplib> (architecture-independent files).
195 =item C<--with-piplib-exec-prefix>
197 Installation prefix for C<system> C<piplib> (architecture-dependent files).
199 =item C<--with-piplib-builddir>
201 Location where C<build> C<piplib> was built.
209 =item 4 Install (optional)
217 =head2 Initialization
219 All manipulations of integer sets and relations occur within
220 the context of an C<isl_ctx>.
221 A given C<isl_ctx> can only be used within a single thread.
222 All arguments of a function are required to have been allocated
223 within the same context.
224 There are currently no functions available for moving an object
225 from one C<isl_ctx> to another C<isl_ctx>. This means that
226 there is currently no way of safely moving an object from one
227 thread to another, unless the whole C<isl_ctx> is moved.
229 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
230 freed using C<isl_ctx_free>.
231 All objects allocated within an C<isl_ctx> should be freed
232 before the C<isl_ctx> itself is freed.
234 isl_ctx *isl_ctx_alloc();
235 void isl_ctx_free(isl_ctx *ctx);
239 All operations on integers, mainly the coefficients
240 of the constraints describing the sets and relations,
241 are performed in exact integer arithmetic using C<GMP>.
242 However, to allow future versions of C<isl> to optionally
243 support fixed integer arithmetic, all calls to C<GMP>
244 are wrapped inside C<isl> specific macros.
245 The basic type is C<isl_int> and the operations below
246 are available on this type.
247 The meanings of these operations are essentially the same
248 as their C<GMP> C<mpz_> counterparts.
249 As always with C<GMP> types, C<isl_int>s need to be
250 initialized with C<isl_int_init> before they can be used
251 and they need to be released with C<isl_int_clear>
253 The user should not assume that an C<isl_int> is represented
254 as a C<mpz_t>, but should instead explicitly convert between
255 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
256 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
260 =item isl_int_init(i)
262 =item isl_int_clear(i)
264 =item isl_int_set(r,i)
266 =item isl_int_set_si(r,i)
268 =item isl_int_set_gmp(r,g)
270 =item isl_int_get_gmp(i,g)
272 =item isl_int_abs(r,i)
274 =item isl_int_neg(r,i)
276 =item isl_int_swap(i,j)
278 =item isl_int_swap_or_set(i,j)
280 =item isl_int_add_ui(r,i,j)
282 =item isl_int_sub_ui(r,i,j)
284 =item isl_int_add(r,i,j)
286 =item isl_int_sub(r,i,j)
288 =item isl_int_mul(r,i,j)
290 =item isl_int_mul_ui(r,i,j)
292 =item isl_int_addmul(r,i,j)
294 =item isl_int_submul(r,i,j)
296 =item isl_int_gcd(r,i,j)
298 =item isl_int_lcm(r,i,j)
300 =item isl_int_divexact(r,i,j)
302 =item isl_int_cdiv_q(r,i,j)
304 =item isl_int_fdiv_q(r,i,j)
306 =item isl_int_fdiv_r(r,i,j)
308 =item isl_int_fdiv_q_ui(r,i,j)
310 =item isl_int_read(r,s)
312 =item isl_int_print(out,i,width)
316 =item isl_int_cmp(i,j)
318 =item isl_int_cmp_si(i,si)
320 =item isl_int_eq(i,j)
322 =item isl_int_ne(i,j)
324 =item isl_int_lt(i,j)
326 =item isl_int_le(i,j)
328 =item isl_int_gt(i,j)
330 =item isl_int_ge(i,j)
332 =item isl_int_abs_eq(i,j)
334 =item isl_int_abs_ne(i,j)
336 =item isl_int_abs_lt(i,j)
338 =item isl_int_abs_gt(i,j)
340 =item isl_int_abs_ge(i,j)
342 =item isl_int_is_zero(i)
344 =item isl_int_is_one(i)
346 =item isl_int_is_negone(i)
348 =item isl_int_is_pos(i)
350 =item isl_int_is_neg(i)
352 =item isl_int_is_nonpos(i)
354 =item isl_int_is_nonneg(i)
356 =item isl_int_is_divisible_by(i,j)
360 =head2 Sets and Relations
362 C<isl> uses six types of objects for representing sets and relations,
363 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
364 C<isl_union_set> and C<isl_union_map>.
365 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
366 can be described as a conjunction of affine constraints, while
367 C<isl_set> and C<isl_map> represent unions of
368 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
369 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
370 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
371 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
372 where dimensions with different space names
373 (see L<Dimension Specifications>) are considered different as well.
374 The difference between sets and relations (maps) is that sets have
375 one set of variables, while relations have two sets of variables,
376 input variables and output variables.
378 =head2 Memory Management
380 Since a high-level operation on sets and/or relations usually involves
381 several substeps and since the user is usually not interested in
382 the intermediate results, most functions that return a new object
383 will also release all the objects passed as arguments.
384 If the user still wants to use one or more of these arguments
385 after the function call, she should pass along a copy of the
386 object rather than the object itself.
387 The user is then responsible for making sure that the original
388 object gets used somewhere else or is explicitly freed.
390 The arguments and return values of all documented functions are
391 annotated to make clear which arguments are released and which
392 arguments are preserved. In particular, the following annotations
399 C<__isl_give> means that a new object is returned.
400 The user should make sure that the returned pointer is
401 used exactly once as a value for an C<__isl_take> argument.
402 In between, it can be used as a value for as many
403 C<__isl_keep> arguments as the user likes.
404 There is one exception, and that is the case where the
405 pointer returned is C<NULL>. Is this case, the user
406 is free to use it as an C<__isl_take> argument or not.
410 C<__isl_take> means that the object the argument points to
411 is taken over by the function and may no longer be used
412 by the user as an argument to any other function.
413 The pointer value must be one returned by a function
414 returning an C<__isl_give> pointer.
415 If the user passes in a C<NULL> value, then this will
416 be treated as an error in the sense that the function will
417 not perform its usual operation. However, it will still
418 make sure that all the other C<__isl_take> arguments
423 C<__isl_keep> means that the function will only use the object
424 temporarily. After the function has finished, the user
425 can still use it as an argument to other functions.
426 A C<NULL> value will be treated in the same way as
427 a C<NULL> value for an C<__isl_take> argument.
433 Identifiers are used to identify both individual dimensions
434 and tuples of dimensions. They consist of a name and an optional
435 pointer. Identifiers with the same name but different pointer values
436 are considered to be distinct.
437 Identifiers can be constructed, copied, freed, inspected and printed
438 using the following functions.
441 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
442 __isl_keep const char *name, void *user);
443 __isl_give isl_id *isl_id_copy(isl_id *id);
444 void *isl_id_free(__isl_take isl_id *id);
446 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
447 void *isl_id_get_user(__isl_keep isl_id *id);
448 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
450 __isl_give isl_printer *isl_printer_print_id(
451 __isl_take isl_printer *p, __isl_keep isl_id *id);
453 Note that C<isl_id_get_name> returns a pointer to some internal
454 data structure, so the result can only be used while the
455 corresponding C<isl_id> is alive.
457 =head2 Dimension Specifications
459 Whenever a new set or relation is created from scratch,
460 its dimension needs to be specified using an C<isl_dim>.
463 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
464 unsigned nparam, unsigned n_in, unsigned n_out);
465 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
466 unsigned nparam, unsigned dim);
467 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
468 void isl_dim_free(__isl_take isl_dim *dim);
469 unsigned isl_dim_size(__isl_keep isl_dim *dim,
470 enum isl_dim_type type);
472 The dimension specification used for creating a set
473 needs to be created using C<isl_dim_set_alloc>, while
474 that for creating a relation
475 needs to be created using C<isl_dim_alloc>.
476 C<isl_dim_size> can be used
477 to find out the number of dimensions of each type in
478 a dimension specification, where type may be
479 C<isl_dim_param>, C<isl_dim_in> (only for relations),
480 C<isl_dim_out> (only for relations), C<isl_dim_set>
481 (only for sets) or C<isl_dim_all>.
483 It is often useful to create objects that live in the
484 same space as some other object. This can be accomplished
485 by creating the new objects
486 (see L<Creating New Sets and Relations> or
487 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
488 specification of the original object.
491 __isl_give isl_dim *isl_basic_set_get_dim(
492 __isl_keep isl_basic_set *bset);
493 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
495 #include <isl/union_set.h>
496 __isl_give isl_dim *isl_union_set_get_dim(
497 __isl_keep isl_union_set *uset);
500 __isl_give isl_dim *isl_basic_map_get_dim(
501 __isl_keep isl_basic_map *bmap);
502 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
504 #include <isl/union_map.h>
505 __isl_give isl_dim *isl_union_map_get_dim(
506 __isl_keep isl_union_map *umap);
508 #include <isl/constraint.h>
509 __isl_give isl_dim *isl_constraint_get_dim(
510 __isl_keep isl_constraint *constraint);
512 #include <isl/polynomial.h>
513 __isl_give isl_dim *isl_qpolynomial_get_dim(
514 __isl_keep isl_qpolynomial *qp);
515 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
516 __isl_keep isl_qpolynomial_fold *fold);
517 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
518 __isl_keep isl_pw_qpolynomial *pwqp);
519 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
520 __isl_keep isl_union_pw_qpolynomial *upwqp);
521 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
522 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
525 __isl_give isl_dim *isl_aff_get_dim(
526 __isl_keep isl_aff *aff);
527 __isl_give isl_dim *isl_pw_aff_get_dim(
528 __isl_keep isl_pw_aff *pwaff);
530 #include <isl/point.h>
531 __isl_give isl_dim *isl_point_get_dim(
532 __isl_keep isl_point *pnt);
534 The identifiers or names of the individual dimensions may be set or read off
535 using the following functions.
538 __isl_give isl_dim *isl_dim_set_dim_id(
539 __isl_take isl_dim *dim,
540 enum isl_dim_type type, unsigned pos,
541 __isl_take isl_id *id);
542 int isl_dim_has_dim_id(__isl_keep isl_dim *dim,
543 enum isl_dim_type type, unsigned pos);
544 __isl_give isl_id *isl_dim_get_dim_id(
545 __isl_keep isl_dim *dim,
546 enum isl_dim_type type, unsigned pos);
547 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
548 enum isl_dim_type type, unsigned pos,
549 __isl_keep const char *name);
550 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
551 enum isl_dim_type type, unsigned pos);
553 Note that C<isl_dim_get_name> returns a pointer to some internal
554 data structure, so the result can only be used while the
555 corresponding C<isl_dim> is alive.
556 Also note that every function that operates on two sets or relations
557 requires that both arguments have the same parameters. This also
558 means that if one of the arguments has named parameters, then the
559 other needs to have named parameters too and the names need to match.
560 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
561 arguments may have different parameters (as long as they are named),
562 in which case the result will have as parameters the union of the parameters of
565 Given the identifier of a dimension (typically a parameter),
566 its position can be obtained from the following function.
569 int isl_dim_find_dim_by_id(__isl_keep isl_dim *dim,
570 enum isl_dim_type type, __isl_keep isl_id *id);
572 The identifiers or names of entire spaces may be set or read off
573 using the following functions.
576 __isl_give isl_dim *isl_dim_set_tuple_id(
577 __isl_take isl_dim *dim,
578 enum isl_dim_type type, __isl_take isl_id *id);
579 __isl_give isl_dim *isl_dim_reset_tuple_id(
580 __isl_take isl_dim *dim, enum isl_dim_type type);
581 __isl_give isl_id *isl_dim_get_tuple_id(
582 __isl_keep isl_dim *dim, enum isl_dim_type type);
583 __isl_give isl_dim *isl_dim_set_tuple_name(
584 __isl_take isl_dim *dim,
585 enum isl_dim_type type, const char *s);
586 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
587 enum isl_dim_type type);
589 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
590 or C<isl_dim_set>. As with C<isl_dim_get_name>,
591 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
593 Binary operations require the corresponding spaces of their arguments
594 to have the same name.
596 Spaces can be nested. In particular, the domain of a set or
597 the domain or range of a relation can be a nested relation.
598 The following functions can be used to construct and deconstruct
599 such nested dimension specifications.
602 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
603 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
604 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
606 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
607 be the dimension specification of a set, while that of
608 C<isl_dim_wrap> should be the dimension specification of a relation.
609 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
610 of a relation, while that of C<isl_dim_wrap> is the dimension specification
613 Dimension specifications can be created from other dimension
614 specifications using the following functions.
616 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
617 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
618 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
619 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
620 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
621 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
622 __isl_take isl_dim *right);
623 __isl_give isl_dim *isl_dim_align_params(
624 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
625 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
626 enum isl_dim_type type, unsigned pos, unsigned n);
627 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
628 enum isl_dim_type type, unsigned n);
629 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
630 enum isl_dim_type type, unsigned first, unsigned n);
631 __isl_give isl_dim *isl_dim_map_from_set(
632 __isl_take isl_dim *dim);
633 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
635 Note that if dimensions are added or removed from a space, then
636 the name and the internal structure are lost.
640 A local space is essentially a dimension specification with
641 zero or more existentially quantified variables.
642 The local space of a basic set or relation can be obtained
643 using the following functions.
646 __isl_give isl_local_space *isl_basic_set_get_local_space(
647 __isl_keep isl_basic_set *bset);
650 __isl_give isl_local_space *isl_basic_map_get_local_space(
651 __isl_keep isl_basic_map *bmap);
653 A new local space can be created from a dimension specification using
655 #include <isl/local_space.h>
656 __isl_give isl_local_space *isl_local_space_from_dim(
657 __isl_take isl_dim *dim);
659 They can be inspected, copied and freed using the following functions.
661 #include <isl/local_space.h>
662 isl_ctx *isl_local_space_get_ctx(
663 __isl_keep isl_local_space *ls);
664 int isl_local_space_dim(__isl_keep isl_local_space *ls,
665 enum isl_dim_type type);
666 const char *isl_local_space_get_dim_name(
667 __isl_keep isl_local_space *ls,
668 enum isl_dim_type type, unsigned pos);
669 __isl_give isl_local_space *isl_local_space_set_dim_name(
670 __isl_take isl_local_space *ls,
671 enum isl_dim_type type, unsigned pos, const char *s);
672 __isl_give isl_dim *isl_local_space_get_dim(
673 __isl_keep isl_local_space *ls);
674 __isl_give isl_div *isl_local_space_get_div(
675 __isl_keep isl_local_space *ls, int pos);
676 __isl_give isl_local_space *isl_local_space_copy(
677 __isl_keep isl_local_space *ls);
678 void *isl_local_space_free(__isl_take isl_local_space *ls);
680 Two local spaces can be compared using
682 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
683 __isl_keep isl_local_space *ls2);
685 Local spaces can be created from other local spaces
686 using the following functions.
688 __isl_give isl_local_space *isl_local_space_from_domain(
689 __isl_take isl_local_space *ls);
690 __isl_give isl_local_space *isl_local_space_add_dims(
691 __isl_take isl_local_space *ls,
692 enum isl_dim_type type, unsigned n);
693 __isl_give isl_local_space *isl_local_space_insert_dims(
694 __isl_take isl_local_space *ls,
695 enum isl_dim_type type, unsigned first, unsigned n);
696 __isl_give isl_local_space *isl_local_space_drop_dims(
697 __isl_take isl_local_space *ls,
698 enum isl_dim_type type, unsigned first, unsigned n);
700 =head2 Input and Output
702 C<isl> supports its own input/output format, which is similar
703 to the C<Omega> format, but also supports the C<PolyLib> format
708 The C<isl> format is similar to that of C<Omega>, but has a different
709 syntax for describing the parameters and allows for the definition
710 of an existentially quantified variable as the integer division
711 of an affine expression.
712 For example, the set of integers C<i> between C<0> and C<n>
713 such that C<i % 10 <= 6> can be described as
715 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
718 A set or relation can have several disjuncts, separated
719 by the keyword C<or>. Each disjunct is either a conjunction
720 of constraints or a projection (C<exists>) of a conjunction
721 of constraints. The constraints are separated by the keyword
724 =head3 C<PolyLib> format
726 If the represented set is a union, then the first line
727 contains a single number representing the number of disjuncts.
728 Otherwise, a line containing the number C<1> is optional.
730 Each disjunct is represented by a matrix of constraints.
731 The first line contains two numbers representing
732 the number of rows and columns,
733 where the number of rows is equal to the number of constraints
734 and the number of columns is equal to two plus the number of variables.
735 The following lines contain the actual rows of the constraint matrix.
736 In each row, the first column indicates whether the constraint
737 is an equality (C<0>) or inequality (C<1>). The final column
738 corresponds to the constant term.
740 If the set is parametric, then the coefficients of the parameters
741 appear in the last columns before the constant column.
742 The coefficients of any existentially quantified variables appear
743 between those of the set variables and those of the parameters.
745 =head3 Extended C<PolyLib> format
747 The extended C<PolyLib> format is nearly identical to the
748 C<PolyLib> format. The only difference is that the line
749 containing the number of rows and columns of a constraint matrix
750 also contains four additional numbers:
751 the number of output dimensions, the number of input dimensions,
752 the number of local dimensions (i.e., the number of existentially
753 quantified variables) and the number of parameters.
754 For sets, the number of ``output'' dimensions is equal
755 to the number of set dimensions, while the number of ``input''
761 __isl_give isl_basic_set *isl_basic_set_read_from_file(
762 isl_ctx *ctx, FILE *input, int nparam);
763 __isl_give isl_basic_set *isl_basic_set_read_from_str(
764 isl_ctx *ctx, const char *str, int nparam);
765 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
766 FILE *input, int nparam);
767 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
768 const char *str, int nparam);
771 __isl_give isl_basic_map *isl_basic_map_read_from_file(
772 isl_ctx *ctx, FILE *input, int nparam);
773 __isl_give isl_basic_map *isl_basic_map_read_from_str(
774 isl_ctx *ctx, const char *str, int nparam);
775 __isl_give isl_map *isl_map_read_from_file(
776 isl_ctx *ctx, FILE *input, int nparam);
777 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
778 const char *str, int nparam);
780 #include <isl/union_set.h>
781 __isl_give isl_union_set *isl_union_set_read_from_file(
782 isl_ctx *ctx, FILE *input);
783 __isl_give isl_union_set *isl_union_set_read_from_str(
784 isl_ctx *ctx, const char *str);
786 #include <isl/union_map.h>
787 __isl_give isl_union_map *isl_union_map_read_from_file(
788 isl_ctx *ctx, FILE *input);
789 __isl_give isl_union_map *isl_union_map_read_from_str(
790 isl_ctx *ctx, const char *str);
792 The input format is autodetected and may be either the C<PolyLib> format
793 or the C<isl> format.
794 C<nparam> specifies how many of the final columns in
795 the C<PolyLib> format correspond to parameters.
796 If input is given in the C<isl> format, then the number
797 of parameters needs to be equal to C<nparam>.
798 If C<nparam> is negative, then any number of parameters
799 is accepted in the C<isl> format and zero parameters
800 are assumed in the C<PolyLib> format.
804 Before anything can be printed, an C<isl_printer> needs to
807 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
809 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
810 void isl_printer_free(__isl_take isl_printer *printer);
811 __isl_give char *isl_printer_get_str(
812 __isl_keep isl_printer *printer);
814 The behavior of the printer can be modified in various ways
816 __isl_give isl_printer *isl_printer_set_output_format(
817 __isl_take isl_printer *p, int output_format);
818 __isl_give isl_printer *isl_printer_set_indent(
819 __isl_take isl_printer *p, int indent);
820 __isl_give isl_printer *isl_printer_indent(
821 __isl_take isl_printer *p, int indent);
822 __isl_give isl_printer *isl_printer_set_prefix(
823 __isl_take isl_printer *p, const char *prefix);
824 __isl_give isl_printer *isl_printer_set_suffix(
825 __isl_take isl_printer *p, const char *suffix);
827 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
828 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
829 and defaults to C<ISL_FORMAT_ISL>.
830 Each line in the output is indented by C<indent> (set by
831 C<isl_printer_set_indent>) spaces
832 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
833 In the C<PolyLib> format output,
834 the coefficients of the existentially quantified variables
835 appear between those of the set variables and those
837 The function C<isl_printer_indent> increases the indentation
838 by the specified amount (which may be negative).
840 To actually print something, use
843 __isl_give isl_printer *isl_printer_print_basic_set(
844 __isl_take isl_printer *printer,
845 __isl_keep isl_basic_set *bset);
846 __isl_give isl_printer *isl_printer_print_set(
847 __isl_take isl_printer *printer,
848 __isl_keep isl_set *set);
851 __isl_give isl_printer *isl_printer_print_basic_map(
852 __isl_take isl_printer *printer,
853 __isl_keep isl_basic_map *bmap);
854 __isl_give isl_printer *isl_printer_print_map(
855 __isl_take isl_printer *printer,
856 __isl_keep isl_map *map);
858 #include <isl/union_set.h>
859 __isl_give isl_printer *isl_printer_print_union_set(
860 __isl_take isl_printer *p,
861 __isl_keep isl_union_set *uset);
863 #include <isl/union_map.h>
864 __isl_give isl_printer *isl_printer_print_union_map(
865 __isl_take isl_printer *p,
866 __isl_keep isl_union_map *umap);
868 When called on a file printer, the following function flushes
869 the file. When called on a string printer, the buffer is cleared.
871 __isl_give isl_printer *isl_printer_flush(
872 __isl_take isl_printer *p);
874 =head2 Creating New Sets and Relations
876 C<isl> has functions for creating some standard sets and relations.
880 =item * Empty sets and relations
882 __isl_give isl_basic_set *isl_basic_set_empty(
883 __isl_take isl_dim *dim);
884 __isl_give isl_basic_map *isl_basic_map_empty(
885 __isl_take isl_dim *dim);
886 __isl_give isl_set *isl_set_empty(
887 __isl_take isl_dim *dim);
888 __isl_give isl_map *isl_map_empty(
889 __isl_take isl_dim *dim);
890 __isl_give isl_union_set *isl_union_set_empty(
891 __isl_take isl_dim *dim);
892 __isl_give isl_union_map *isl_union_map_empty(
893 __isl_take isl_dim *dim);
895 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
896 is only used to specify the parameters.
898 =item * Universe sets and relations
900 __isl_give isl_basic_set *isl_basic_set_universe(
901 __isl_take isl_dim *dim);
902 __isl_give isl_basic_map *isl_basic_map_universe(
903 __isl_take isl_dim *dim);
904 __isl_give isl_set *isl_set_universe(
905 __isl_take isl_dim *dim);
906 __isl_give isl_map *isl_map_universe(
907 __isl_take isl_dim *dim);
908 __isl_give isl_union_set *isl_union_set_universe(
909 __isl_take isl_union_set *uset);
910 __isl_give isl_union_map *isl_union_map_universe(
911 __isl_take isl_union_map *umap);
913 The sets and relations constructed by the functions above
914 contain all integer values, while those constructed by the
915 functions below only contain non-negative values.
917 __isl_give isl_basic_set *isl_basic_set_nat_universe(
918 __isl_take isl_dim *dim);
919 __isl_give isl_basic_map *isl_basic_map_nat_universe(
920 __isl_take isl_dim *dim);
921 __isl_give isl_set *isl_set_nat_universe(
922 __isl_take isl_dim *dim);
923 __isl_give isl_map *isl_map_nat_universe(
924 __isl_take isl_dim *dim);
926 =item * Identity relations
928 __isl_give isl_basic_map *isl_basic_map_identity(
929 __isl_take isl_dim *dim);
930 __isl_give isl_map *isl_map_identity(
931 __isl_take isl_dim *dim);
933 The number of input and output dimensions in C<dim> needs
936 =item * Lexicographic order
938 __isl_give isl_map *isl_map_lex_lt(
939 __isl_take isl_dim *set_dim);
940 __isl_give isl_map *isl_map_lex_le(
941 __isl_take isl_dim *set_dim);
942 __isl_give isl_map *isl_map_lex_gt(
943 __isl_take isl_dim *set_dim);
944 __isl_give isl_map *isl_map_lex_ge(
945 __isl_take isl_dim *set_dim);
946 __isl_give isl_map *isl_map_lex_lt_first(
947 __isl_take isl_dim *dim, unsigned n);
948 __isl_give isl_map *isl_map_lex_le_first(
949 __isl_take isl_dim *dim, unsigned n);
950 __isl_give isl_map *isl_map_lex_gt_first(
951 __isl_take isl_dim *dim, unsigned n);
952 __isl_give isl_map *isl_map_lex_ge_first(
953 __isl_take isl_dim *dim, unsigned n);
955 The first four functions take a dimension specification for a B<set>
956 and return relations that express that the elements in the domain
957 are lexicographically less
958 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
959 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
960 than the elements in the range.
961 The last four functions take a dimension specification for a map
962 and return relations that express that the first C<n> dimensions
963 in the domain are lexicographically less
964 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
965 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
966 than the first C<n> dimensions in the range.
970 A basic set or relation can be converted to a set or relation
971 using the following functions.
973 __isl_give isl_set *isl_set_from_basic_set(
974 __isl_take isl_basic_set *bset);
975 __isl_give isl_map *isl_map_from_basic_map(
976 __isl_take isl_basic_map *bmap);
978 Sets and relations can be converted to union sets and relations
979 using the following functions.
981 __isl_give isl_union_map *isl_union_map_from_map(
982 __isl_take isl_map *map);
983 __isl_give isl_union_set *isl_union_set_from_set(
984 __isl_take isl_set *set);
986 The inverse conversions below can only be used if the input
987 union set or relation is known to contain elements in exactly one
990 __isl_give isl_set *isl_set_from_union_set(
991 __isl_take isl_union_set *uset);
992 __isl_give isl_map *isl_map_from_union_map(
993 __isl_take isl_union_map *umap);
995 Sets and relations can be copied and freed again using the following
998 __isl_give isl_basic_set *isl_basic_set_copy(
999 __isl_keep isl_basic_set *bset);
1000 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1001 __isl_give isl_union_set *isl_union_set_copy(
1002 __isl_keep isl_union_set *uset);
1003 __isl_give isl_basic_map *isl_basic_map_copy(
1004 __isl_keep isl_basic_map *bmap);
1005 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1006 __isl_give isl_union_map *isl_union_map_copy(
1007 __isl_keep isl_union_map *umap);
1008 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1009 void isl_set_free(__isl_take isl_set *set);
1010 void *isl_union_set_free(__isl_take isl_union_set *uset);
1011 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1012 void isl_map_free(__isl_take isl_map *map);
1013 void *isl_union_map_free(__isl_take isl_union_map *umap);
1015 Other sets and relations can be constructed by starting
1016 from a universe set or relation, adding equality and/or
1017 inequality constraints and then projecting out the
1018 existentially quantified variables, if any.
1019 Constraints can be constructed, manipulated and
1020 added to (or removed from) (basic) sets and relations
1021 using the following functions.
1023 #include <isl/constraint.h>
1024 __isl_give isl_constraint *isl_equality_alloc(
1025 __isl_take isl_dim *dim);
1026 __isl_give isl_constraint *isl_inequality_alloc(
1027 __isl_take isl_dim *dim);
1028 __isl_give isl_constraint *isl_constraint_set_constant(
1029 __isl_take isl_constraint *constraint, isl_int v);
1030 __isl_give isl_constraint *isl_constraint_set_constant_si(
1031 __isl_take isl_constraint *constraint, int v);
1032 __isl_give isl_constraint *isl_constraint_set_coefficient(
1033 __isl_take isl_constraint *constraint,
1034 enum isl_dim_type type, int pos, isl_int v);
1035 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1036 __isl_take isl_constraint *constraint,
1037 enum isl_dim_type type, int pos, int v);
1038 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1039 __isl_take isl_basic_map *bmap,
1040 __isl_take isl_constraint *constraint);
1041 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1042 __isl_take isl_basic_set *bset,
1043 __isl_take isl_constraint *constraint);
1044 __isl_give isl_map *isl_map_add_constraint(
1045 __isl_take isl_map *map,
1046 __isl_take isl_constraint *constraint);
1047 __isl_give isl_set *isl_set_add_constraint(
1048 __isl_take isl_set *set,
1049 __isl_take isl_constraint *constraint);
1050 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1051 __isl_take isl_basic_set *bset,
1052 __isl_take isl_constraint *constraint);
1054 For example, to create a set containing the even integers
1055 between 10 and 42, you would use the following code.
1060 isl_basic_set *bset;
1063 dim = isl_dim_set_alloc(ctx, 0, 2);
1064 bset = isl_basic_set_universe(isl_dim_copy(dim));
1066 c = isl_equality_alloc(isl_dim_copy(dim));
1067 isl_int_set_si(v, -1);
1068 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1069 isl_int_set_si(v, 2);
1070 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1071 bset = isl_basic_set_add_constraint(bset, c);
1073 c = isl_inequality_alloc(isl_dim_copy(dim));
1074 isl_int_set_si(v, -10);
1075 isl_constraint_set_constant(c, v);
1076 isl_int_set_si(v, 1);
1077 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1078 bset = isl_basic_set_add_constraint(bset, c);
1080 c = isl_inequality_alloc(dim);
1081 isl_int_set_si(v, 42);
1082 isl_constraint_set_constant(c, v);
1083 isl_int_set_si(v, -1);
1084 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1085 bset = isl_basic_set_add_constraint(bset, c);
1087 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1093 isl_basic_set *bset;
1094 bset = isl_basic_set_read_from_str(ctx,
1095 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1097 A basic set or relation can also be constructed from two matrices
1098 describing the equalities and the inequalities.
1100 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1101 __isl_take isl_dim *dim,
1102 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1103 enum isl_dim_type c1,
1104 enum isl_dim_type c2, enum isl_dim_type c3,
1105 enum isl_dim_type c4);
1106 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1107 __isl_take isl_dim *dim,
1108 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1109 enum isl_dim_type c1,
1110 enum isl_dim_type c2, enum isl_dim_type c3,
1111 enum isl_dim_type c4, enum isl_dim_type c5);
1113 The C<isl_dim_type> arguments indicate the order in which
1114 different kinds of variables appear in the input matrices
1115 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1116 C<isl_dim_set> and C<isl_dim_div> for sets and
1117 of C<isl_dim_cst>, C<isl_dim_param>,
1118 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1120 A (basic) relation can also be constructed from a (piecewise) affine expression
1121 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1123 __isl_give isl_basic_map *isl_basic_map_from_aff(
1124 __isl_take isl_aff *aff);
1125 __isl_give isl_map *isl_map_from_pw_aff(
1126 __isl_take isl_pw_aff *pwaff);
1127 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1128 __isl_take isl_dim *domain_dim,
1129 __isl_take isl_aff_list *list);
1131 The C<domain_dim> argument describes the domain of the resulting
1132 basic relation. It is required because the C<list> may consist
1133 of zero affine expressions.
1135 =head2 Inspecting Sets and Relations
1137 Usually, the user should not have to care about the actual constraints
1138 of the sets and maps, but should instead apply the abstract operations
1139 explained in the following sections.
1140 Occasionally, however, it may be required to inspect the individual
1141 coefficients of the constraints. This section explains how to do so.
1142 In these cases, it may also be useful to have C<isl> compute
1143 an explicit representation of the existentially quantified variables.
1145 __isl_give isl_set *isl_set_compute_divs(
1146 __isl_take isl_set *set);
1147 __isl_give isl_map *isl_map_compute_divs(
1148 __isl_take isl_map *map);
1149 __isl_give isl_union_set *isl_union_set_compute_divs(
1150 __isl_take isl_union_set *uset);
1151 __isl_give isl_union_map *isl_union_map_compute_divs(
1152 __isl_take isl_union_map *umap);
1154 This explicit representation defines the existentially quantified
1155 variables as integer divisions of the other variables, possibly
1156 including earlier existentially quantified variables.
1157 An explicitly represented existentially quantified variable therefore
1158 has a unique value when the values of the other variables are known.
1159 If, furthermore, the same existentials, i.e., existentials
1160 with the same explicit representations, should appear in the
1161 same order in each of the disjuncts of a set or map, then the user should call
1162 either of the following functions.
1164 __isl_give isl_set *isl_set_align_divs(
1165 __isl_take isl_set *set);
1166 __isl_give isl_map *isl_map_align_divs(
1167 __isl_take isl_map *map);
1169 Alternatively, the existentially quantified variables can be removed
1170 using the following functions, which compute an overapproximation.
1172 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1173 __isl_take isl_basic_set *bset);
1174 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1175 __isl_take isl_basic_map *bmap);
1176 __isl_give isl_set *isl_set_remove_divs(
1177 __isl_take isl_set *set);
1178 __isl_give isl_map *isl_map_remove_divs(
1179 __isl_take isl_map *map);
1181 To iterate over all the sets or maps in a union set or map, use
1183 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1184 int (*fn)(__isl_take isl_set *set, void *user),
1186 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1187 int (*fn)(__isl_take isl_map *map, void *user),
1190 The number of sets or maps in a union set or map can be obtained
1193 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1194 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1196 To extract the set or map from a union with a given dimension
1199 __isl_give isl_set *isl_union_set_extract_set(
1200 __isl_keep isl_union_set *uset,
1201 __isl_take isl_dim *dim);
1202 __isl_give isl_map *isl_union_map_extract_map(
1203 __isl_keep isl_union_map *umap,
1204 __isl_take isl_dim *dim);
1206 To iterate over all the basic sets or maps in a set or map, use
1208 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1209 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1211 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1212 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1215 The callback function C<fn> should return 0 if successful and
1216 -1 if an error occurs. In the latter case, or if any other error
1217 occurs, the above functions will return -1.
1219 It should be noted that C<isl> does not guarantee that
1220 the basic sets or maps passed to C<fn> are disjoint.
1221 If this is required, then the user should call one of
1222 the following functions first.
1224 __isl_give isl_set *isl_set_make_disjoint(
1225 __isl_take isl_set *set);
1226 __isl_give isl_map *isl_map_make_disjoint(
1227 __isl_take isl_map *map);
1229 The number of basic sets in a set can be obtained
1232 int isl_set_n_basic_set(__isl_keep isl_set *set);
1234 To iterate over the constraints of a basic set or map, use
1236 #include <isl/constraint.h>
1238 int isl_basic_map_foreach_constraint(
1239 __isl_keep isl_basic_map *bmap,
1240 int (*fn)(__isl_take isl_constraint *c, void *user),
1242 void *isl_constraint_free(__isl_take isl_constraint *c);
1244 Again, the callback function C<fn> should return 0 if successful and
1245 -1 if an error occurs. In the latter case, or if any other error
1246 occurs, the above functions will return -1.
1247 The constraint C<c> represents either an equality or an inequality.
1248 Use the following function to find out whether a constraint
1249 represents an equality. If not, it represents an inequality.
1251 int isl_constraint_is_equality(
1252 __isl_keep isl_constraint *constraint);
1254 The coefficients of the constraints can be inspected using
1255 the following functions.
1257 void isl_constraint_get_constant(
1258 __isl_keep isl_constraint *constraint, isl_int *v);
1259 void isl_constraint_get_coefficient(
1260 __isl_keep isl_constraint *constraint,
1261 enum isl_dim_type type, int pos, isl_int *v);
1262 int isl_constraint_involves_dims(
1263 __isl_keep isl_constraint *constraint,
1264 enum isl_dim_type type, unsigned first, unsigned n);
1266 The explicit representations of the existentially quantified
1267 variables can be inspected using the following functions.
1268 Note that the user is only allowed to use these functions
1269 if the inspected set or map is the result of a call
1270 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1272 __isl_give isl_div *isl_constraint_div(
1273 __isl_keep isl_constraint *constraint, int pos);
1274 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1275 void isl_div_get_constant(__isl_keep isl_div *div,
1277 void isl_div_get_denominator(__isl_keep isl_div *div,
1279 void isl_div_get_coefficient(__isl_keep isl_div *div,
1280 enum isl_dim_type type, int pos, isl_int *v);
1282 To obtain the constraints of a basic set or map in matrix
1283 form, use the following functions.
1285 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1286 __isl_keep isl_basic_set *bset,
1287 enum isl_dim_type c1, enum isl_dim_type c2,
1288 enum isl_dim_type c3, enum isl_dim_type c4);
1289 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1290 __isl_keep isl_basic_set *bset,
1291 enum isl_dim_type c1, enum isl_dim_type c2,
1292 enum isl_dim_type c3, enum isl_dim_type c4);
1293 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1294 __isl_keep isl_basic_map *bmap,
1295 enum isl_dim_type c1,
1296 enum isl_dim_type c2, enum isl_dim_type c3,
1297 enum isl_dim_type c4, enum isl_dim_type c5);
1298 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1299 __isl_keep isl_basic_map *bmap,
1300 enum isl_dim_type c1,
1301 enum isl_dim_type c2, enum isl_dim_type c3,
1302 enum isl_dim_type c4, enum isl_dim_type c5);
1304 The C<isl_dim_type> arguments dictate the order in which
1305 different kinds of variables appear in the resulting matrix
1306 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1307 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1309 The number of parameters, input, output or set dimensions can
1310 be obtained using the following functions.
1312 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1313 enum isl_dim_type type);
1314 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1315 enum isl_dim_type type);
1316 unsigned isl_set_dim(__isl_keep isl_set *set,
1317 enum isl_dim_type type);
1318 unsigned isl_map_dim(__isl_keep isl_map *map,
1319 enum isl_dim_type type);
1321 To check whether the description of a set or relation depends
1322 on one or more given dimensions, it is not necessary to iterate over all
1323 constraints. Instead the following functions can be used.
1325 int isl_basic_set_involves_dims(
1326 __isl_keep isl_basic_set *bset,
1327 enum isl_dim_type type, unsigned first, unsigned n);
1328 int isl_set_involves_dims(__isl_keep isl_set *set,
1329 enum isl_dim_type type, unsigned first, unsigned n);
1330 int isl_basic_map_involves_dims(
1331 __isl_keep isl_basic_map *bmap,
1332 enum isl_dim_type type, unsigned first, unsigned n);
1333 int isl_map_involves_dims(__isl_keep isl_map *map,
1334 enum isl_dim_type type, unsigned first, unsigned n);
1336 Similarly, the following functions can be used to check whether
1337 a given dimension is involved in any lower or upper bound.
1339 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1340 enum isl_dim_type type, unsigned pos);
1341 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1342 enum isl_dim_type type, unsigned pos);
1344 The identifiers or names of the domain and range spaces of a set
1345 or relation can be read off or set using the following functions.
1347 __isl_give isl_set *isl_set_set_tuple_id(
1348 __isl_take isl_set *set, __isl_take isl_id *id);
1349 __isl_give isl_set *isl_set_reset_tuple_id(
1350 __isl_take isl_set *set);
1351 __isl_give isl_id *isl_set_get_tuple_id(
1352 __isl_keep isl_set *set);
1353 __isl_give isl_map *isl_map_set_tuple_id(
1354 __isl_take isl_map *map, enum isl_dim_type type,
1355 __isl_take isl_id *id);
1356 __isl_give isl_map *isl_map_reset_tuple_id(
1357 __isl_take isl_map *map, enum isl_dim_type type);
1358 __isl_give isl_id *isl_map_get_tuple_id(
1359 __isl_keep isl_map *map, enum isl_dim_type type);
1361 const char *isl_basic_set_get_tuple_name(
1362 __isl_keep isl_basic_set *bset);
1363 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1364 __isl_take isl_basic_set *set, const char *s);
1365 const char *isl_set_get_tuple_name(
1366 __isl_keep isl_set *set);
1367 const char *isl_basic_map_get_tuple_name(
1368 __isl_keep isl_basic_map *bmap,
1369 enum isl_dim_type type);
1370 const char *isl_map_get_tuple_name(
1371 __isl_keep isl_map *map,
1372 enum isl_dim_type type);
1374 As with C<isl_dim_get_tuple_name>, the value returned points to
1375 an internal data structure.
1376 The identifiers, positions or names of individual dimensions can be
1377 read off using the following functions.
1379 __isl_give isl_set *isl_set_set_dim_id(
1380 __isl_take isl_set *set, enum isl_dim_type type,
1381 unsigned pos, __isl_take isl_id *id);
1382 int isl_set_has_dim_id(__isl_keep isl_set *set,
1383 enum isl_dim_type type, unsigned pos);
1384 __isl_give isl_id *isl_set_get_dim_id(
1385 __isl_keep isl_set *set, enum isl_dim_type type,
1387 __isl_give isl_map *isl_map_set_dim_id(
1388 __isl_take isl_map *map, enum isl_dim_type type,
1389 unsigned pos, __isl_take isl_id *id);
1390 int isl_map_has_dim_id(__isl_keep isl_map *map,
1391 enum isl_dim_type type, unsigned pos);
1392 __isl_give isl_id *isl_map_get_dim_id(
1393 __isl_keep isl_map *map, enum isl_dim_type type,
1396 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1397 enum isl_dim_type type, __isl_keep isl_id *id);
1398 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1399 enum isl_dim_type type, __isl_keep isl_id *id);
1401 const char *isl_constraint_get_dim_name(
1402 __isl_keep isl_constraint *constraint,
1403 enum isl_dim_type type, unsigned pos);
1404 const char *isl_basic_set_get_dim_name(
1405 __isl_keep isl_basic_set *bset,
1406 enum isl_dim_type type, unsigned pos);
1407 const char *isl_set_get_dim_name(
1408 __isl_keep isl_set *set,
1409 enum isl_dim_type type, unsigned pos);
1410 const char *isl_basic_map_get_dim_name(
1411 __isl_keep isl_basic_map *bmap,
1412 enum isl_dim_type type, unsigned pos);
1413 const char *isl_map_get_dim_name(
1414 __isl_keep isl_map *map,
1415 enum isl_dim_type type, unsigned pos);
1417 These functions are mostly useful to obtain the identifiers, positions
1418 or names of the parameters. Identifiers of individual dimensions are
1419 essentially only useful for printing. They are ignored by all other
1420 operations and may not be preserved across those operations.
1424 =head3 Unary Properties
1430 The following functions test whether the given set or relation
1431 contains any integer points. The ``plain'' variants do not perform
1432 any computations, but simply check if the given set or relation
1433 is already known to be empty.
1435 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1436 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1437 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1438 int isl_set_is_empty(__isl_keep isl_set *set);
1439 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1440 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1441 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1442 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1443 int isl_map_is_empty(__isl_keep isl_map *map);
1444 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1446 =item * Universality
1448 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1449 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1450 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1452 =item * Single-valuedness
1454 int isl_map_is_single_valued(__isl_keep isl_map *map);
1455 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1459 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1460 int isl_map_is_injective(__isl_keep isl_map *map);
1461 int isl_union_map_plain_is_injective(
1462 __isl_keep isl_union_map *umap);
1463 int isl_union_map_is_injective(
1464 __isl_keep isl_union_map *umap);
1468 int isl_map_is_bijective(__isl_keep isl_map *map);
1469 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1473 int isl_basic_map_plain_is_fixed(
1474 __isl_keep isl_basic_map *bmap,
1475 enum isl_dim_type type, unsigned pos,
1477 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1478 enum isl_dim_type type, unsigned pos,
1481 Check if the relation obviously lies on a hyperplane where the given dimension
1482 has a fixed value and if so, return that value in C<*val>.
1486 The following functions check whether the domain of the given
1487 (basic) set is a wrapped relation.
1489 int isl_basic_set_is_wrapping(
1490 __isl_keep isl_basic_set *bset);
1491 int isl_set_is_wrapping(__isl_keep isl_set *set);
1493 =item * Internal Product
1495 int isl_basic_map_can_zip(
1496 __isl_keep isl_basic_map *bmap);
1497 int isl_map_can_zip(__isl_keep isl_map *map);
1499 Check whether the product of domain and range of the given relation
1501 i.e., whether both domain and range are nested relations.
1505 =head3 Binary Properties
1511 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1512 __isl_keep isl_set *set2);
1513 int isl_set_is_equal(__isl_keep isl_set *set1,
1514 __isl_keep isl_set *set2);
1515 int isl_union_set_is_equal(
1516 __isl_keep isl_union_set *uset1,
1517 __isl_keep isl_union_set *uset2);
1518 int isl_basic_map_is_equal(
1519 __isl_keep isl_basic_map *bmap1,
1520 __isl_keep isl_basic_map *bmap2);
1521 int isl_map_is_equal(__isl_keep isl_map *map1,
1522 __isl_keep isl_map *map2);
1523 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1524 __isl_keep isl_map *map2);
1525 int isl_union_map_is_equal(
1526 __isl_keep isl_union_map *umap1,
1527 __isl_keep isl_union_map *umap2);
1529 =item * Disjointness
1531 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1532 __isl_keep isl_set *set2);
1536 int isl_set_is_subset(__isl_keep isl_set *set1,
1537 __isl_keep isl_set *set2);
1538 int isl_set_is_strict_subset(
1539 __isl_keep isl_set *set1,
1540 __isl_keep isl_set *set2);
1541 int isl_union_set_is_subset(
1542 __isl_keep isl_union_set *uset1,
1543 __isl_keep isl_union_set *uset2);
1544 int isl_union_set_is_strict_subset(
1545 __isl_keep isl_union_set *uset1,
1546 __isl_keep isl_union_set *uset2);
1547 int isl_basic_map_is_subset(
1548 __isl_keep isl_basic_map *bmap1,
1549 __isl_keep isl_basic_map *bmap2);
1550 int isl_basic_map_is_strict_subset(
1551 __isl_keep isl_basic_map *bmap1,
1552 __isl_keep isl_basic_map *bmap2);
1553 int isl_map_is_subset(
1554 __isl_keep isl_map *map1,
1555 __isl_keep isl_map *map2);
1556 int isl_map_is_strict_subset(
1557 __isl_keep isl_map *map1,
1558 __isl_keep isl_map *map2);
1559 int isl_union_map_is_subset(
1560 __isl_keep isl_union_map *umap1,
1561 __isl_keep isl_union_map *umap2);
1562 int isl_union_map_is_strict_subset(
1563 __isl_keep isl_union_map *umap1,
1564 __isl_keep isl_union_map *umap2);
1568 =head2 Unary Operations
1574 __isl_give isl_set *isl_set_complement(
1575 __isl_take isl_set *set);
1579 __isl_give isl_basic_map *isl_basic_map_reverse(
1580 __isl_take isl_basic_map *bmap);
1581 __isl_give isl_map *isl_map_reverse(
1582 __isl_take isl_map *map);
1583 __isl_give isl_union_map *isl_union_map_reverse(
1584 __isl_take isl_union_map *umap);
1588 __isl_give isl_basic_set *isl_basic_set_project_out(
1589 __isl_take isl_basic_set *bset,
1590 enum isl_dim_type type, unsigned first, unsigned n);
1591 __isl_give isl_basic_map *isl_basic_map_project_out(
1592 __isl_take isl_basic_map *bmap,
1593 enum isl_dim_type type, unsigned first, unsigned n);
1594 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1595 enum isl_dim_type type, unsigned first, unsigned n);
1596 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1597 enum isl_dim_type type, unsigned first, unsigned n);
1598 __isl_give isl_basic_set *isl_basic_map_domain(
1599 __isl_take isl_basic_map *bmap);
1600 __isl_give isl_basic_set *isl_basic_map_range(
1601 __isl_take isl_basic_map *bmap);
1602 __isl_give isl_set *isl_map_domain(
1603 __isl_take isl_map *bmap);
1604 __isl_give isl_set *isl_map_range(
1605 __isl_take isl_map *map);
1606 __isl_give isl_union_set *isl_union_map_domain(
1607 __isl_take isl_union_map *umap);
1608 __isl_give isl_union_set *isl_union_map_range(
1609 __isl_take isl_union_map *umap);
1611 __isl_give isl_basic_map *isl_basic_map_domain_map(
1612 __isl_take isl_basic_map *bmap);
1613 __isl_give isl_basic_map *isl_basic_map_range_map(
1614 __isl_take isl_basic_map *bmap);
1615 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1616 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1617 __isl_give isl_union_map *isl_union_map_domain_map(
1618 __isl_take isl_union_map *umap);
1619 __isl_give isl_union_map *isl_union_map_range_map(
1620 __isl_take isl_union_map *umap);
1622 The functions above construct a (basic, regular or union) relation
1623 that maps (a wrapped version of) the input relation to its domain or range.
1627 __isl_give isl_set *isl_set_eliminate(
1628 __isl_take isl_set *set, enum isl_dim_type type,
1629 unsigned first, unsigned n);
1631 Eliminate the coefficients for the given dimensions from the constraints,
1632 without removing the dimensions.
1636 __isl_give isl_basic_set *isl_basic_set_fix(
1637 __isl_take isl_basic_set *bset,
1638 enum isl_dim_type type, unsigned pos,
1640 __isl_give isl_basic_set *isl_basic_set_fix_si(
1641 __isl_take isl_basic_set *bset,
1642 enum isl_dim_type type, unsigned pos, int value);
1643 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1644 enum isl_dim_type type, unsigned pos,
1646 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1647 enum isl_dim_type type, unsigned pos, int value);
1648 __isl_give isl_basic_map *isl_basic_map_fix_si(
1649 __isl_take isl_basic_map *bmap,
1650 enum isl_dim_type type, unsigned pos, int value);
1651 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1652 enum isl_dim_type type, unsigned pos, int value);
1654 Intersect the set or relation with the hyperplane where the given
1655 dimension has the fixed given value.
1657 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1658 enum isl_dim_type type1, int pos1,
1659 enum isl_dim_type type2, int pos2);
1660 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1661 enum isl_dim_type type1, int pos1,
1662 enum isl_dim_type type2, int pos2);
1664 Intersect the set or relation with the hyperplane where the given
1665 dimensions are equal to each other.
1667 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1668 enum isl_dim_type type1, int pos1,
1669 enum isl_dim_type type2, int pos2);
1671 Intersect the relation with the hyperplane where the given
1672 dimensions have opposite values.
1676 __isl_give isl_map *isl_set_identity(
1677 __isl_take isl_set *set);
1678 __isl_give isl_union_map *isl_union_set_identity(
1679 __isl_take isl_union_set *uset);
1681 Construct an identity relation on the given (union) set.
1685 __isl_give isl_basic_set *isl_basic_map_deltas(
1686 __isl_take isl_basic_map *bmap);
1687 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1688 __isl_give isl_union_set *isl_union_map_deltas(
1689 __isl_take isl_union_map *umap);
1691 These functions return a (basic) set containing the differences
1692 between image elements and corresponding domain elements in the input.
1694 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1695 __isl_take isl_basic_map *bmap);
1696 __isl_give isl_map *isl_map_deltas_map(
1697 __isl_take isl_map *map);
1698 __isl_give isl_union_map *isl_union_map_deltas_map(
1699 __isl_take isl_union_map *umap);
1701 The functions above construct a (basic, regular or union) relation
1702 that maps (a wrapped version of) the input relation to its delta set.
1706 Simplify the representation of a set or relation by trying
1707 to combine pairs of basic sets or relations into a single
1708 basic set or relation.
1710 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1711 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1712 __isl_give isl_union_set *isl_union_set_coalesce(
1713 __isl_take isl_union_set *uset);
1714 __isl_give isl_union_map *isl_union_map_coalesce(
1715 __isl_take isl_union_map *umap);
1717 =item * Detecting equalities
1719 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1720 __isl_take isl_basic_set *bset);
1721 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1722 __isl_take isl_basic_map *bmap);
1723 __isl_give isl_set *isl_set_detect_equalities(
1724 __isl_take isl_set *set);
1725 __isl_give isl_map *isl_map_detect_equalities(
1726 __isl_take isl_map *map);
1727 __isl_give isl_union_set *isl_union_set_detect_equalities(
1728 __isl_take isl_union_set *uset);
1729 __isl_give isl_union_map *isl_union_map_detect_equalities(
1730 __isl_take isl_union_map *umap);
1732 Simplify the representation of a set or relation by detecting implicit
1735 =item * Removing redundant constraints
1737 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1738 __isl_take isl_basic_set *bset);
1739 __isl_give isl_set *isl_set_remove_redundancies(
1740 __isl_take isl_set *set);
1741 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1742 __isl_take isl_basic_map *bmap);
1743 __isl_give isl_map *isl_map_remove_redundancies(
1744 __isl_take isl_map *map);
1748 __isl_give isl_basic_set *isl_set_convex_hull(
1749 __isl_take isl_set *set);
1750 __isl_give isl_basic_map *isl_map_convex_hull(
1751 __isl_take isl_map *map);
1753 If the input set or relation has any existentially quantified
1754 variables, then the result of these operations is currently undefined.
1758 __isl_give isl_basic_set *isl_set_simple_hull(
1759 __isl_take isl_set *set);
1760 __isl_give isl_basic_map *isl_map_simple_hull(
1761 __isl_take isl_map *map);
1762 __isl_give isl_union_map *isl_union_map_simple_hull(
1763 __isl_take isl_union_map *umap);
1765 These functions compute a single basic set or relation
1766 that contains the whole input set or relation.
1767 In particular, the output is described by translates
1768 of the constraints describing the basic sets or relations in the input.
1772 (See \autoref{s:simple hull}.)
1778 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1779 __isl_take isl_basic_set *bset);
1780 __isl_give isl_basic_set *isl_set_affine_hull(
1781 __isl_take isl_set *set);
1782 __isl_give isl_union_set *isl_union_set_affine_hull(
1783 __isl_take isl_union_set *uset);
1784 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1785 __isl_take isl_basic_map *bmap);
1786 __isl_give isl_basic_map *isl_map_affine_hull(
1787 __isl_take isl_map *map);
1788 __isl_give isl_union_map *isl_union_map_affine_hull(
1789 __isl_take isl_union_map *umap);
1791 In case of union sets and relations, the affine hull is computed
1794 =item * Polyhedral hull
1796 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1797 __isl_take isl_set *set);
1798 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1799 __isl_take isl_map *map);
1800 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1801 __isl_take isl_union_set *uset);
1802 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1803 __isl_take isl_union_map *umap);
1805 These functions compute a single basic set or relation
1806 not involving any existentially quantified variables
1807 that contains the whole input set or relation.
1808 In case of union sets and relations, the polyhedral hull is computed
1811 =item * Optimization
1813 #include <isl/ilp.h>
1814 enum isl_lp_result isl_basic_set_max(
1815 __isl_keep isl_basic_set *bset,
1816 __isl_keep isl_aff *obj, isl_int *opt)
1817 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1818 __isl_keep isl_aff *obj, isl_int *opt);
1819 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1820 __isl_keep isl_aff *obj, isl_int *opt);
1822 Compute the minimum or maximum of the integer affine expression C<obj>
1823 over the points in C<set>, returning the result in C<opt>.
1824 The return value may be one of C<isl_lp_error>,
1825 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1827 =item * Parametric optimization
1829 __isl_give isl_pw_aff *isl_set_dim_max(
1830 __isl_take isl_set *set, int pos);
1832 Compute the maximum of the given set dimension as a function of the
1833 parameters, but independently of the other set dimensions.
1834 For lexicographic optimization, see L<"Lexicographic Optimization">.
1838 The following functions compute either the set of (rational) coefficient
1839 values of valid constraints for the given set or the set of (rational)
1840 values satisfying the constraints with coefficients from the given set.
1841 Internally, these two sets of functions perform essentially the
1842 same operations, except that the set of coefficients is assumed to
1843 be a cone, while the set of values may be any polyhedron.
1844 The current implementation is based on the Farkas lemma and
1845 Fourier-Motzkin elimination, but this may change or be made optional
1846 in future. In particular, future implementations may use different
1847 dualization algorithms or skip the elimination step.
1849 __isl_give isl_basic_set *isl_basic_set_coefficients(
1850 __isl_take isl_basic_set *bset);
1851 __isl_give isl_basic_set *isl_set_coefficients(
1852 __isl_take isl_set *set);
1853 __isl_give isl_union_set *isl_union_set_coefficients(
1854 __isl_take isl_union_set *bset);
1855 __isl_give isl_basic_set *isl_basic_set_solutions(
1856 __isl_take isl_basic_set *bset);
1857 __isl_give isl_basic_set *isl_set_solutions(
1858 __isl_take isl_set *set);
1859 __isl_give isl_union_set *isl_union_set_solutions(
1860 __isl_take isl_union_set *bset);
1864 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1866 __isl_give isl_union_map *isl_union_map_power(
1867 __isl_take isl_union_map *umap, int *exact);
1869 Compute a parametric representation for all positive powers I<k> of C<map>.
1870 The result maps I<k> to a nested relation corresponding to the
1871 I<k>th power of C<map>.
1872 The result may be an overapproximation. If the result is known to be exact,
1873 then C<*exact> is set to C<1>.
1875 =item * Transitive closure
1877 __isl_give isl_map *isl_map_transitive_closure(
1878 __isl_take isl_map *map, int *exact);
1879 __isl_give isl_union_map *isl_union_map_transitive_closure(
1880 __isl_take isl_union_map *umap, int *exact);
1882 Compute the transitive closure of C<map>.
1883 The result may be an overapproximation. If the result is known to be exact,
1884 then C<*exact> is set to C<1>.
1886 =item * Reaching path lengths
1888 __isl_give isl_map *isl_map_reaching_path_lengths(
1889 __isl_take isl_map *map, int *exact);
1891 Compute a relation that maps each element in the range of C<map>
1892 to the lengths of all paths composed of edges in C<map> that
1893 end up in the given element.
1894 The result may be an overapproximation. If the result is known to be exact,
1895 then C<*exact> is set to C<1>.
1896 To compute the I<maximal> path length, the resulting relation
1897 should be postprocessed by C<isl_map_lexmax>.
1898 In particular, if the input relation is a dependence relation
1899 (mapping sources to sinks), then the maximal path length corresponds
1900 to the free schedule.
1901 Note, however, that C<isl_map_lexmax> expects the maximum to be
1902 finite, so if the path lengths are unbounded (possibly due to
1903 the overapproximation), then you will get an error message.
1907 __isl_give isl_basic_set *isl_basic_map_wrap(
1908 __isl_take isl_basic_map *bmap);
1909 __isl_give isl_set *isl_map_wrap(
1910 __isl_take isl_map *map);
1911 __isl_give isl_union_set *isl_union_map_wrap(
1912 __isl_take isl_union_map *umap);
1913 __isl_give isl_basic_map *isl_basic_set_unwrap(
1914 __isl_take isl_basic_set *bset);
1915 __isl_give isl_map *isl_set_unwrap(
1916 __isl_take isl_set *set);
1917 __isl_give isl_union_map *isl_union_set_unwrap(
1918 __isl_take isl_union_set *uset);
1922 Remove any internal structure of domain (and range) of the given
1923 set or relation. If there is any such internal structure in the input,
1924 then the name of the space is also removed.
1926 __isl_give isl_basic_set *isl_basic_set_flatten(
1927 __isl_take isl_basic_set *bset);
1928 __isl_give isl_set *isl_set_flatten(
1929 __isl_take isl_set *set);
1930 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1931 __isl_take isl_basic_map *bmap);
1932 __isl_give isl_map *isl_map_flatten_range(
1933 __isl_take isl_map *map);
1934 __isl_give isl_basic_map *isl_basic_map_flatten(
1935 __isl_take isl_basic_map *bmap);
1936 __isl_give isl_map *isl_map_flatten(
1937 __isl_take isl_map *map);
1939 __isl_give isl_map *isl_set_flatten_map(
1940 __isl_take isl_set *set);
1942 The function above constructs a relation
1943 that maps the input set to a flattened version of the set.
1947 Lift the input set to a space with extra dimensions corresponding
1948 to the existentially quantified variables in the input.
1949 In particular, the result lives in a wrapped map where the domain
1950 is the original space and the range corresponds to the original
1951 existentially quantified variables.
1953 __isl_give isl_basic_set *isl_basic_set_lift(
1954 __isl_take isl_basic_set *bset);
1955 __isl_give isl_set *isl_set_lift(
1956 __isl_take isl_set *set);
1957 __isl_give isl_union_set *isl_union_set_lift(
1958 __isl_take isl_union_set *uset);
1960 =item * Internal Product
1962 __isl_give isl_basic_map *isl_basic_map_zip(
1963 __isl_take isl_basic_map *bmap);
1964 __isl_give isl_map *isl_map_zip(
1965 __isl_take isl_map *map);
1966 __isl_give isl_union_map *isl_union_map_zip(
1967 __isl_take isl_union_map *umap);
1969 Given a relation with nested relations for domain and range,
1970 interchange the range of the domain with the domain of the range.
1972 =item * Aligning parameters
1974 __isl_give isl_set *isl_set_align_params(
1975 __isl_take isl_set *set,
1976 __isl_take isl_dim *model);
1977 __isl_give isl_map *isl_map_align_params(
1978 __isl_take isl_map *map,
1979 __isl_take isl_dim *model);
1981 Change the order of the parameters of the given set or relation
1982 such that the first parameters match those of C<model>.
1983 This may involve the introduction of extra parameters.
1984 All parameters need to be named.
1986 =item * Dimension manipulation
1988 __isl_give isl_set *isl_set_add_dims(
1989 __isl_take isl_set *set,
1990 enum isl_dim_type type, unsigned n);
1991 __isl_give isl_map *isl_map_add_dims(
1992 __isl_take isl_map *map,
1993 enum isl_dim_type type, unsigned n);
1994 __isl_give isl_set *isl_set_insert_dims(
1995 __isl_take isl_set *set,
1996 enum isl_dim_type type, unsigned pos, unsigned n);
1997 __isl_give isl_map *isl_map_insert_dims(
1998 __isl_take isl_map *map,
1999 enum isl_dim_type type, unsigned pos, unsigned n);
2001 It is usually not advisable to directly change the (input or output)
2002 space of a set or a relation as this removes the name and the internal
2003 structure of the space. However, the above functions can be useful
2004 to add new parameters, assuming
2005 C<isl_set_align_params> and C<isl_map_align_params>
2010 =head2 Binary Operations
2012 The two arguments of a binary operation not only need to live
2013 in the same C<isl_ctx>, they currently also need to have
2014 the same (number of) parameters.
2016 =head3 Basic Operations
2020 =item * Intersection
2022 __isl_give isl_basic_set *isl_basic_set_intersect(
2023 __isl_take isl_basic_set *bset1,
2024 __isl_take isl_basic_set *bset2);
2025 __isl_give isl_set *isl_set_intersect_params(
2026 __isl_take isl_set *set,
2027 __isl_take isl_set *params);
2028 __isl_give isl_set *isl_set_intersect(
2029 __isl_take isl_set *set1,
2030 __isl_take isl_set *set2);
2031 __isl_give isl_union_set *isl_union_set_intersect(
2032 __isl_take isl_union_set *uset1,
2033 __isl_take isl_union_set *uset2);
2034 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2035 __isl_take isl_basic_map *bmap,
2036 __isl_take isl_basic_set *bset);
2037 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2038 __isl_take isl_basic_map *bmap,
2039 __isl_take isl_basic_set *bset);
2040 __isl_give isl_basic_map *isl_basic_map_intersect(
2041 __isl_take isl_basic_map *bmap1,
2042 __isl_take isl_basic_map *bmap2);
2043 __isl_give isl_map *isl_map_intersect_params(
2044 __isl_take isl_map *map,
2045 __isl_take isl_set *params);
2046 __isl_give isl_map *isl_map_intersect_domain(
2047 __isl_take isl_map *map,
2048 __isl_take isl_set *set);
2049 __isl_give isl_map *isl_map_intersect_range(
2050 __isl_take isl_map *map,
2051 __isl_take isl_set *set);
2052 __isl_give isl_map *isl_map_intersect(
2053 __isl_take isl_map *map1,
2054 __isl_take isl_map *map2);
2055 __isl_give isl_union_map *isl_union_map_intersect_domain(
2056 __isl_take isl_union_map *umap,
2057 __isl_take isl_union_set *uset);
2058 __isl_give isl_union_map *isl_union_map_intersect_range(
2059 __isl_take isl_union_map *umap,
2060 __isl_take isl_union_set *uset);
2061 __isl_give isl_union_map *isl_union_map_intersect(
2062 __isl_take isl_union_map *umap1,
2063 __isl_take isl_union_map *umap2);
2067 __isl_give isl_set *isl_basic_set_union(
2068 __isl_take isl_basic_set *bset1,
2069 __isl_take isl_basic_set *bset2);
2070 __isl_give isl_map *isl_basic_map_union(
2071 __isl_take isl_basic_map *bmap1,
2072 __isl_take isl_basic_map *bmap2);
2073 __isl_give isl_set *isl_set_union(
2074 __isl_take isl_set *set1,
2075 __isl_take isl_set *set2);
2076 __isl_give isl_map *isl_map_union(
2077 __isl_take isl_map *map1,
2078 __isl_take isl_map *map2);
2079 __isl_give isl_union_set *isl_union_set_union(
2080 __isl_take isl_union_set *uset1,
2081 __isl_take isl_union_set *uset2);
2082 __isl_give isl_union_map *isl_union_map_union(
2083 __isl_take isl_union_map *umap1,
2084 __isl_take isl_union_map *umap2);
2086 =item * Set difference
2088 __isl_give isl_set *isl_set_subtract(
2089 __isl_take isl_set *set1,
2090 __isl_take isl_set *set2);
2091 __isl_give isl_map *isl_map_subtract(
2092 __isl_take isl_map *map1,
2093 __isl_take isl_map *map2);
2094 __isl_give isl_union_set *isl_union_set_subtract(
2095 __isl_take isl_union_set *uset1,
2096 __isl_take isl_union_set *uset2);
2097 __isl_give isl_union_map *isl_union_map_subtract(
2098 __isl_take isl_union_map *umap1,
2099 __isl_take isl_union_map *umap2);
2103 __isl_give isl_basic_set *isl_basic_set_apply(
2104 __isl_take isl_basic_set *bset,
2105 __isl_take isl_basic_map *bmap);
2106 __isl_give isl_set *isl_set_apply(
2107 __isl_take isl_set *set,
2108 __isl_take isl_map *map);
2109 __isl_give isl_union_set *isl_union_set_apply(
2110 __isl_take isl_union_set *uset,
2111 __isl_take isl_union_map *umap);
2112 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2113 __isl_take isl_basic_map *bmap1,
2114 __isl_take isl_basic_map *bmap2);
2115 __isl_give isl_basic_map *isl_basic_map_apply_range(
2116 __isl_take isl_basic_map *bmap1,
2117 __isl_take isl_basic_map *bmap2);
2118 __isl_give isl_map *isl_map_apply_domain(
2119 __isl_take isl_map *map1,
2120 __isl_take isl_map *map2);
2121 __isl_give isl_union_map *isl_union_map_apply_domain(
2122 __isl_take isl_union_map *umap1,
2123 __isl_take isl_union_map *umap2);
2124 __isl_give isl_map *isl_map_apply_range(
2125 __isl_take isl_map *map1,
2126 __isl_take isl_map *map2);
2127 __isl_give isl_union_map *isl_union_map_apply_range(
2128 __isl_take isl_union_map *umap1,
2129 __isl_take isl_union_map *umap2);
2131 =item * Cartesian Product
2133 __isl_give isl_set *isl_set_product(
2134 __isl_take isl_set *set1,
2135 __isl_take isl_set *set2);
2136 __isl_give isl_union_set *isl_union_set_product(
2137 __isl_take isl_union_set *uset1,
2138 __isl_take isl_union_set *uset2);
2139 __isl_give isl_basic_map *isl_basic_map_range_product(
2140 __isl_take isl_basic_map *bmap1,
2141 __isl_take isl_basic_map *bmap2);
2142 __isl_give isl_map *isl_map_range_product(
2143 __isl_take isl_map *map1,
2144 __isl_take isl_map *map2);
2145 __isl_give isl_union_map *isl_union_map_range_product(
2146 __isl_take isl_union_map *umap1,
2147 __isl_take isl_union_map *umap2);
2148 __isl_give isl_map *isl_map_product(
2149 __isl_take isl_map *map1,
2150 __isl_take isl_map *map2);
2151 __isl_give isl_union_map *isl_union_map_product(
2152 __isl_take isl_union_map *umap1,
2153 __isl_take isl_union_map *umap2);
2155 The above functions compute the cross product of the given
2156 sets or relations. The domains and ranges of the results
2157 are wrapped maps between domains and ranges of the inputs.
2158 To obtain a ``flat'' product, use the following functions
2161 __isl_give isl_basic_set *isl_basic_set_flat_product(
2162 __isl_take isl_basic_set *bset1,
2163 __isl_take isl_basic_set *bset2);
2164 __isl_give isl_set *isl_set_flat_product(
2165 __isl_take isl_set *set1,
2166 __isl_take isl_set *set2);
2167 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2168 __isl_take isl_basic_map *bmap1,
2169 __isl_take isl_basic_map *bmap2);
2170 __isl_give isl_map *isl_map_flat_range_product(
2171 __isl_take isl_map *map1,
2172 __isl_take isl_map *map2);
2173 __isl_give isl_union_map *isl_union_map_flat_range_product(
2174 __isl_take isl_union_map *umap1,
2175 __isl_take isl_union_map *umap2);
2176 __isl_give isl_basic_map *isl_basic_map_flat_product(
2177 __isl_take isl_basic_map *bmap1,
2178 __isl_take isl_basic_map *bmap2);
2179 __isl_give isl_map *isl_map_flat_product(
2180 __isl_take isl_map *map1,
2181 __isl_take isl_map *map2);
2183 =item * Simplification
2185 __isl_give isl_basic_set *isl_basic_set_gist(
2186 __isl_take isl_basic_set *bset,
2187 __isl_take isl_basic_set *context);
2188 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2189 __isl_take isl_set *context);
2190 __isl_give isl_union_set *isl_union_set_gist(
2191 __isl_take isl_union_set *uset,
2192 __isl_take isl_union_set *context);
2193 __isl_give isl_basic_map *isl_basic_map_gist(
2194 __isl_take isl_basic_map *bmap,
2195 __isl_take isl_basic_map *context);
2196 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2197 __isl_take isl_map *context);
2198 __isl_give isl_union_map *isl_union_map_gist(
2199 __isl_take isl_union_map *umap,
2200 __isl_take isl_union_map *context);
2202 The gist operation returns a set or relation that has the
2203 same intersection with the context as the input set or relation.
2204 Any implicit equality in the intersection is made explicit in the result,
2205 while all inequalities that are redundant with respect to the intersection
2207 In case of union sets and relations, the gist operation is performed
2212 =head3 Lexicographic Optimization
2214 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2215 the following functions
2216 compute a set that contains the lexicographic minimum or maximum
2217 of the elements in C<set> (or C<bset>) for those values of the parameters
2218 that satisfy C<dom>.
2219 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2220 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2222 In other words, the union of the parameter values
2223 for which the result is non-empty and of C<*empty>
2226 __isl_give isl_set *isl_basic_set_partial_lexmin(
2227 __isl_take isl_basic_set *bset,
2228 __isl_take isl_basic_set *dom,
2229 __isl_give isl_set **empty);
2230 __isl_give isl_set *isl_basic_set_partial_lexmax(
2231 __isl_take isl_basic_set *bset,
2232 __isl_take isl_basic_set *dom,
2233 __isl_give isl_set **empty);
2234 __isl_give isl_set *isl_set_partial_lexmin(
2235 __isl_take isl_set *set, __isl_take isl_set *dom,
2236 __isl_give isl_set **empty);
2237 __isl_give isl_set *isl_set_partial_lexmax(
2238 __isl_take isl_set *set, __isl_take isl_set *dom,
2239 __isl_give isl_set **empty);
2241 Given a (basic) set C<set> (or C<bset>), the following functions simply
2242 return a set containing the lexicographic minimum or maximum
2243 of the elements in C<set> (or C<bset>).
2244 In case of union sets, the optimum is computed per space.
2246 __isl_give isl_set *isl_basic_set_lexmin(
2247 __isl_take isl_basic_set *bset);
2248 __isl_give isl_set *isl_basic_set_lexmax(
2249 __isl_take isl_basic_set *bset);
2250 __isl_give isl_set *isl_set_lexmin(
2251 __isl_take isl_set *set);
2252 __isl_give isl_set *isl_set_lexmax(
2253 __isl_take isl_set *set);
2254 __isl_give isl_union_set *isl_union_set_lexmin(
2255 __isl_take isl_union_set *uset);
2256 __isl_give isl_union_set *isl_union_set_lexmax(
2257 __isl_take isl_union_set *uset);
2259 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2260 the following functions
2261 compute a relation that maps each element of C<dom>
2262 to the single lexicographic minimum or maximum
2263 of the elements that are associated to that same
2264 element in C<map> (or C<bmap>).
2265 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2266 that contains the elements in C<dom> that do not map
2267 to any elements in C<map> (or C<bmap>).
2268 In other words, the union of the domain of the result and of C<*empty>
2271 __isl_give isl_map *isl_basic_map_partial_lexmax(
2272 __isl_take isl_basic_map *bmap,
2273 __isl_take isl_basic_set *dom,
2274 __isl_give isl_set **empty);
2275 __isl_give isl_map *isl_basic_map_partial_lexmin(
2276 __isl_take isl_basic_map *bmap,
2277 __isl_take isl_basic_set *dom,
2278 __isl_give isl_set **empty);
2279 __isl_give isl_map *isl_map_partial_lexmax(
2280 __isl_take isl_map *map, __isl_take isl_set *dom,
2281 __isl_give isl_set **empty);
2282 __isl_give isl_map *isl_map_partial_lexmin(
2283 __isl_take isl_map *map, __isl_take isl_set *dom,
2284 __isl_give isl_set **empty);
2286 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2287 return a map mapping each element in the domain of
2288 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2289 of all elements associated to that element.
2290 In case of union relations, the optimum is computed per space.
2292 __isl_give isl_map *isl_basic_map_lexmin(
2293 __isl_take isl_basic_map *bmap);
2294 __isl_give isl_map *isl_basic_map_lexmax(
2295 __isl_take isl_basic_map *bmap);
2296 __isl_give isl_map *isl_map_lexmin(
2297 __isl_take isl_map *map);
2298 __isl_give isl_map *isl_map_lexmax(
2299 __isl_take isl_map *map);
2300 __isl_give isl_union_map *isl_union_map_lexmin(
2301 __isl_take isl_union_map *umap);
2302 __isl_give isl_union_map *isl_union_map_lexmax(
2303 __isl_take isl_union_map *umap);
2307 Lists are defined over several element types, including
2308 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2309 Here we take lists of C<isl_set>s as an example.
2310 Lists can be created, copied and freed using the following functions.
2312 #include <isl/list.h>
2313 __isl_give isl_set_list *isl_set_list_from_set(
2314 __isl_take isl_set *el);
2315 __isl_give isl_set_list *isl_set_list_alloc(
2316 isl_ctx *ctx, int n);
2317 __isl_give isl_set_list *isl_set_list_copy(
2318 __isl_keep isl_set_list *list);
2319 __isl_give isl_set_list *isl_set_list_add(
2320 __isl_take isl_set_list *list,
2321 __isl_take isl_set *el);
2322 __isl_give isl_set_list *isl_set_list_concat(
2323 __isl_take isl_set_list *list1,
2324 __isl_take isl_set_list *list2);
2325 void *isl_set_list_free(__isl_take isl_set_list *list);
2327 C<isl_set_list_alloc> creates an empty list with a capacity for
2328 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2331 Lists can be inspected using the following functions.
2333 #include <isl/list.h>
2334 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2335 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2336 __isl_give isl_set *isl_set_list_get_set(
2337 __isl_keep isl_set_list *list, int index);
2338 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2339 int (*fn)(__isl_take isl_set *el, void *user),
2342 Lists can be printed using
2344 #include <isl/list.h>
2345 __isl_give isl_printer *isl_printer_print_set_list(
2346 __isl_take isl_printer *p,
2347 __isl_keep isl_set_list *list);
2351 Matrices can be created, copied and freed using the following functions.
2353 #include <isl/mat.h>
2354 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2355 unsigned n_row, unsigned n_col);
2356 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2357 void isl_mat_free(__isl_take isl_mat *mat);
2359 Note that the elements of a newly created matrix may have arbitrary values.
2360 The elements can be changed and inspected using the following functions.
2362 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2363 int isl_mat_rows(__isl_keep isl_mat *mat);
2364 int isl_mat_cols(__isl_keep isl_mat *mat);
2365 int isl_mat_get_element(__isl_keep isl_mat *mat,
2366 int row, int col, isl_int *v);
2367 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2368 int row, int col, isl_int v);
2369 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2370 int row, int col, int v);
2372 C<isl_mat_get_element> will return a negative value if anything went wrong.
2373 In that case, the value of C<*v> is undefined.
2375 The following function can be used to compute the (right) inverse
2376 of a matrix, i.e., a matrix such that the product of the original
2377 and the inverse (in that order) is a multiple of the identity matrix.
2378 The input matrix is assumed to be of full row-rank.
2380 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2382 The following function can be used to compute the (right) kernel
2383 (or null space) of a matrix, i.e., a matrix such that the product of
2384 the original and the kernel (in that order) is the zero matrix.
2386 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2388 =head2 Piecewise Quasi Affine Expressions
2390 The zero quasi affine expression can be created using
2392 __isl_give isl_aff *isl_aff_zero(
2393 __isl_take isl_local_space *ls);
2395 A quasi affine expression can also be initialized from an C<isl_div>:
2397 #include <isl/div.h>
2398 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2400 An empty piecewise quasi affine expression (one with no cells)
2401 or a piecewise quasi affine expression with a single cell can
2402 be created using the following functions.
2404 #include <isl/aff.h>
2405 __isl_give isl_pw_aff *isl_pw_aff_empty(
2406 __isl_take isl_dim *dim);
2407 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2408 __isl_take isl_set *set, __isl_take isl_aff *aff);
2409 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2410 __isl_take isl_aff *aff);
2412 Quasi affine expressions can be copied and freed using
2414 #include <isl/aff.h>
2415 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2416 void *isl_aff_free(__isl_take isl_aff *aff);
2418 __isl_give isl_pw_aff *isl_pw_aff_copy(
2419 __isl_keep isl_pw_aff *pwaff);
2420 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2422 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2423 using the following function. The constraint is required to have
2424 a non-zero coefficient for the specified dimension.
2426 #include <isl/constraint.h>
2427 __isl_give isl_aff *isl_constraint_get_bound(
2428 __isl_keep isl_constraint *constraint,
2429 enum isl_dim_type type, int pos);
2431 The entire affine expression of the constraint can also be extracted
2432 using the following function.
2434 #include <isl/constraint.h>
2435 __isl_give isl_aff *isl_constraint_get_aff(
2436 __isl_keep isl_constraint *constraint);
2438 Conversely, an equality constraint equating
2439 the affine expression to zero or an inequality constraint enforcing
2440 the affine expression to be non-negative, can be constructed using
2442 __isl_give isl_constraint *isl_equality_from_aff(
2443 __isl_take isl_aff *aff);
2444 __isl_give isl_constraint *isl_inequality_from_aff(
2445 __isl_take isl_aff *aff);
2447 The expression can be inspected using
2449 #include <isl/aff.h>
2450 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2451 int isl_aff_dim(__isl_keep isl_aff *aff,
2452 enum isl_dim_type type);
2453 __isl_give isl_local_space *isl_aff_get_local_space(
2454 __isl_keep isl_aff *aff);
2455 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2456 enum isl_dim_type type, unsigned pos);
2457 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2459 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2460 enum isl_dim_type type, int pos, isl_int *v);
2461 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2463 __isl_give isl_div *isl_aff_get_div(
2464 __isl_keep isl_aff *aff, int pos);
2466 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2467 int (*fn)(__isl_take isl_set *set,
2468 __isl_take isl_aff *aff,
2469 void *user), void *user);
2471 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2472 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2474 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2475 enum isl_dim_type type, unsigned first, unsigned n);
2476 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2477 enum isl_dim_type type, unsigned first, unsigned n);
2479 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2480 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2481 enum isl_dim_type type);
2482 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2484 It can be modified using
2486 #include <isl/aff.h>
2487 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2488 __isl_take isl_pw_aff *pwaff,
2489 __isl_take isl_id *id);
2490 __isl_give isl_aff *isl_aff_set_dim_name(
2491 __isl_take isl_aff *aff, enum isl_dim_type type,
2492 unsigned pos, const char *s);
2493 __isl_give isl_aff *isl_aff_set_constant(
2494 __isl_take isl_aff *aff, isl_int v);
2495 __isl_give isl_aff *isl_aff_set_constant_si(
2496 __isl_take isl_aff *aff, int v);
2497 __isl_give isl_aff *isl_aff_set_coefficient(
2498 __isl_take isl_aff *aff,
2499 enum isl_dim_type type, int pos, isl_int v);
2500 __isl_give isl_aff *isl_aff_set_coefficient_si(
2501 __isl_take isl_aff *aff,
2502 enum isl_dim_type type, int pos, int v);
2503 __isl_give isl_aff *isl_aff_set_denominator(
2504 __isl_take isl_aff *aff, isl_int v);
2506 __isl_give isl_aff *isl_aff_add_constant(
2507 __isl_take isl_aff *aff, isl_int v);
2508 __isl_give isl_aff *isl_aff_add_constant_si(
2509 __isl_take isl_aff *aff, int v);
2510 __isl_give isl_aff *isl_aff_add_coefficient(
2511 __isl_take isl_aff *aff,
2512 enum isl_dim_type type, int pos, isl_int v);
2513 __isl_give isl_aff *isl_aff_add_coefficient_si(
2514 __isl_take isl_aff *aff,
2515 enum isl_dim_type type, int pos, int v);
2517 __isl_give isl_aff *isl_aff_insert_dims(
2518 __isl_take isl_aff *aff,
2519 enum isl_dim_type type, unsigned first, unsigned n);
2520 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2521 __isl_take isl_pw_aff *pwaff,
2522 enum isl_dim_type type, unsigned first, unsigned n);
2523 __isl_give isl_aff *isl_aff_add_dims(
2524 __isl_take isl_aff *aff,
2525 enum isl_dim_type type, unsigned n);
2526 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2527 __isl_take isl_pw_aff *pwaff,
2528 enum isl_dim_type type, unsigned n);
2529 __isl_give isl_aff *isl_aff_drop_dims(
2530 __isl_take isl_aff *aff,
2531 enum isl_dim_type type, unsigned first, unsigned n);
2532 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2533 __isl_take isl_pw_aff *pwaff,
2534 enum isl_dim_type type, unsigned first, unsigned n);
2536 Note that the C<set_constant> and C<set_coefficient> functions
2537 set the I<numerator> of the constant or coefficient, while
2538 C<add_constant> and C<add_coefficient> add an integer value to
2539 the possibly rational constant or coefficient.
2541 To check whether an affine expressions is obviously zero
2542 or obviously equal to some other affine expression, use
2544 #include <isl/aff.h>
2545 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2546 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2547 __isl_keep isl_aff *aff2);
2551 #include <isl/aff.h>
2552 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2553 __isl_take isl_aff *aff2);
2554 __isl_give isl_pw_aff *isl_pw_aff_add(
2555 __isl_take isl_pw_aff *pwaff1,
2556 __isl_take isl_pw_aff *pwaff2);
2557 __isl_give isl_pw_aff *isl_pw_aff_min(
2558 __isl_take isl_pw_aff *pwaff1,
2559 __isl_take isl_pw_aff *pwaff2);
2560 __isl_give isl_pw_aff *isl_pw_aff_max(
2561 __isl_take isl_pw_aff *pwaff1,
2562 __isl_take isl_pw_aff *pwaff2);
2563 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2564 __isl_take isl_aff *aff2);
2565 __isl_give isl_pw_aff *isl_pw_aff_sub(
2566 __isl_take isl_pw_aff *pwaff1,
2567 __isl_take isl_pw_aff *pwaff2);
2568 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2569 __isl_give isl_pw_aff *isl_pw_aff_neg(
2570 __isl_take isl_pw_aff *pwaff);
2571 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2572 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2573 __isl_take isl_pw_aff *pwaff);
2574 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2575 __isl_give isl_pw_aff *isl_pw_aff_floor(
2576 __isl_take isl_pw_aff *pwaff);
2577 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2579 __isl_give isl_pw_aff *isl_pw_aff_mod(
2580 __isl_take isl_pw_aff *pwaff, isl_int mod);
2581 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2583 __isl_give isl_pw_aff *isl_pw_aff_scale(
2584 __isl_take isl_pw_aff *pwaff, isl_int f);
2585 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2587 __isl_give isl_aff *isl_aff_scale_down_ui(
2588 __isl_take isl_aff *aff, unsigned f);
2589 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2590 __isl_take isl_pw_aff *pwaff, isl_int f);
2592 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2593 __isl_take isl_pw_aff_list *list);
2594 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2595 __isl_take isl_pw_aff_list *list);
2597 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2598 __isl_take isl_pw_aff *pwqp);
2600 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2601 __isl_take isl_pw_aff *pwaff,
2602 __isl_take isl_dim *model);
2604 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2605 __isl_take isl_set *context);
2606 __isl_give isl_pw_aff *isl_pw_aff_gist(
2607 __isl_take isl_pw_aff *pwaff,
2608 __isl_take isl_set *context);
2610 __isl_give isl_set *isl_pw_aff_domain(
2611 __isl_take isl_pw_aff *pwaff);
2613 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2614 __isl_take isl_aff *aff2);
2615 __isl_give isl_pw_aff *isl_pw_aff_mul(
2616 __isl_take isl_pw_aff *pwaff1,
2617 __isl_take isl_pw_aff *pwaff2);
2619 When multiplying two affine expressions, at least one of the two needs
2622 #include <isl/aff.h>
2623 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2624 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2625 __isl_give isl_set *isl_pw_aff_eq_set(
2626 __isl_take isl_pw_aff *pwaff1,
2627 __isl_take isl_pw_aff *pwaff2);
2628 __isl_give isl_set *isl_pw_aff_ne_set(
2629 __isl_take isl_pw_aff *pwaff1,
2630 __isl_take isl_pw_aff *pwaff2);
2631 __isl_give isl_set *isl_pw_aff_le_set(
2632 __isl_take isl_pw_aff *pwaff1,
2633 __isl_take isl_pw_aff *pwaff2);
2634 __isl_give isl_set *isl_pw_aff_lt_set(
2635 __isl_take isl_pw_aff *pwaff1,
2636 __isl_take isl_pw_aff *pwaff2);
2637 __isl_give isl_set *isl_pw_aff_ge_set(
2638 __isl_take isl_pw_aff *pwaff1,
2639 __isl_take isl_pw_aff *pwaff2);
2640 __isl_give isl_set *isl_pw_aff_gt_set(
2641 __isl_take isl_pw_aff *pwaff1,
2642 __isl_take isl_pw_aff *pwaff2);
2644 __isl_give isl_set *isl_pw_aff_list_eq_set(
2645 __isl_take isl_pw_aff_list *list1,
2646 __isl_take isl_pw_aff_list *list2);
2647 __isl_give isl_set *isl_pw_aff_list_ne_set(
2648 __isl_take isl_pw_aff_list *list1,
2649 __isl_take isl_pw_aff_list *list2);
2650 __isl_give isl_set *isl_pw_aff_list_le_set(
2651 __isl_take isl_pw_aff_list *list1,
2652 __isl_take isl_pw_aff_list *list2);
2653 __isl_give isl_set *isl_pw_aff_list_lt_set(
2654 __isl_take isl_pw_aff_list *list1,
2655 __isl_take isl_pw_aff_list *list2);
2656 __isl_give isl_set *isl_pw_aff_list_ge_set(
2657 __isl_take isl_pw_aff_list *list1,
2658 __isl_take isl_pw_aff_list *list2);
2659 __isl_give isl_set *isl_pw_aff_list_gt_set(
2660 __isl_take isl_pw_aff_list *list1,
2661 __isl_take isl_pw_aff_list *list2);
2663 The function C<isl_aff_ge_basic_set> returns a basic set
2664 containing those elements in the shared space
2665 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2666 The function C<isl_aff_ge_set> returns a set
2667 containing those elements in the shared domain
2668 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2669 The functions operating on C<isl_pw_aff_list> apply the corresponding
2670 C<isl_pw_aff> function to each pair of elements in the two lists.
2672 #include <isl/aff.h>
2673 __isl_give isl_set *isl_pw_aff_nonneg_set(
2674 __isl_take isl_pw_aff *pwaff);
2675 __isl_give isl_set *isl_pw_aff_zero_set(
2676 __isl_take isl_pw_aff *pwaff);
2677 __isl_give isl_set *isl_pw_aff_non_zero_set(
2678 __isl_take isl_pw_aff *pwaff);
2680 The function C<isl_pw_aff_nonneg_set> returns a set
2681 containing those elements in the domain
2682 of C<pwaff> where C<pwaff> is non-negative.
2684 #include <isl/aff.h>
2685 __isl_give isl_pw_aff *isl_pw_aff_cond(
2686 __isl_take isl_set *cond,
2687 __isl_take isl_pw_aff *pwaff_true,
2688 __isl_take isl_pw_aff *pwaff_false);
2690 The function C<isl_pw_aff_cond> performs a conditional operator
2691 and returns an expression that is equal to C<pwaff_true>
2692 for elements in C<cond> and equal to C<pwaff_false> for elements
2695 #include <isl/aff.h>
2696 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2697 __isl_take isl_pw_aff *pwaff1,
2698 __isl_take isl_pw_aff *pwaff2);
2700 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2701 expression with a domain that is the union of those of C<pwaff1> and
2702 C<pwaff2> and such that on each cell, the quasi-affine expression is
2703 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2704 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2705 associated expression is the defined one.
2707 An expression can be printed using
2709 #include <isl/aff.h>
2710 __isl_give isl_printer *isl_printer_print_aff(
2711 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2713 __isl_give isl_printer *isl_printer_print_pw_aff(
2714 __isl_take isl_printer *p,
2715 __isl_keep isl_pw_aff *pwaff);
2719 Points are elements of a set. They can be used to construct
2720 simple sets (boxes) or they can be used to represent the
2721 individual elements of a set.
2722 The zero point (the origin) can be created using
2724 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2726 The coordinates of a point can be inspected, set and changed
2729 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2730 enum isl_dim_type type, int pos, isl_int *v);
2731 __isl_give isl_point *isl_point_set_coordinate(
2732 __isl_take isl_point *pnt,
2733 enum isl_dim_type type, int pos, isl_int v);
2735 __isl_give isl_point *isl_point_add_ui(
2736 __isl_take isl_point *pnt,
2737 enum isl_dim_type type, int pos, unsigned val);
2738 __isl_give isl_point *isl_point_sub_ui(
2739 __isl_take isl_point *pnt,
2740 enum isl_dim_type type, int pos, unsigned val);
2742 Other properties can be obtained using
2744 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2746 Points can be copied or freed using
2748 __isl_give isl_point *isl_point_copy(
2749 __isl_keep isl_point *pnt);
2750 void isl_point_free(__isl_take isl_point *pnt);
2752 A singleton set can be created from a point using
2754 __isl_give isl_basic_set *isl_basic_set_from_point(
2755 __isl_take isl_point *pnt);
2756 __isl_give isl_set *isl_set_from_point(
2757 __isl_take isl_point *pnt);
2759 and a box can be created from two opposite extremal points using
2761 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2762 __isl_take isl_point *pnt1,
2763 __isl_take isl_point *pnt2);
2764 __isl_give isl_set *isl_set_box_from_points(
2765 __isl_take isl_point *pnt1,
2766 __isl_take isl_point *pnt2);
2768 All elements of a B<bounded> (union) set can be enumerated using
2769 the following functions.
2771 int isl_set_foreach_point(__isl_keep isl_set *set,
2772 int (*fn)(__isl_take isl_point *pnt, void *user),
2774 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2775 int (*fn)(__isl_take isl_point *pnt, void *user),
2778 The function C<fn> is called for each integer point in
2779 C<set> with as second argument the last argument of
2780 the C<isl_set_foreach_point> call. The function C<fn>
2781 should return C<0> on success and C<-1> on failure.
2782 In the latter case, C<isl_set_foreach_point> will stop
2783 enumerating and return C<-1> as well.
2784 If the enumeration is performed successfully and to completion,
2785 then C<isl_set_foreach_point> returns C<0>.
2787 To obtain a single point of a (basic) set, use
2789 __isl_give isl_point *isl_basic_set_sample_point(
2790 __isl_take isl_basic_set *bset);
2791 __isl_give isl_point *isl_set_sample_point(
2792 __isl_take isl_set *set);
2794 If C<set> does not contain any (integer) points, then the
2795 resulting point will be ``void'', a property that can be
2798 int isl_point_is_void(__isl_keep isl_point *pnt);
2800 =head2 Piecewise Quasipolynomials
2802 A piecewise quasipolynomial is a particular kind of function that maps
2803 a parametric point to a rational value.
2804 More specifically, a quasipolynomial is a polynomial expression in greatest
2805 integer parts of affine expressions of parameters and variables.
2806 A piecewise quasipolynomial is a subdivision of a given parametric
2807 domain into disjoint cells with a quasipolynomial associated to
2808 each cell. The value of the piecewise quasipolynomial at a given
2809 point is the value of the quasipolynomial associated to the cell
2810 that contains the point. Outside of the union of cells,
2811 the value is assumed to be zero.
2812 For example, the piecewise quasipolynomial
2814 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2816 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2817 A given piecewise quasipolynomial has a fixed domain dimension.
2818 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2819 defined over different domains.
2820 Piecewise quasipolynomials are mainly used by the C<barvinok>
2821 library for representing the number of elements in a parametric set or map.
2822 For example, the piecewise quasipolynomial above represents
2823 the number of points in the map
2825 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2827 =head3 Printing (Piecewise) Quasipolynomials
2829 Quasipolynomials and piecewise quasipolynomials can be printed
2830 using the following functions.
2832 __isl_give isl_printer *isl_printer_print_qpolynomial(
2833 __isl_take isl_printer *p,
2834 __isl_keep isl_qpolynomial *qp);
2836 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2837 __isl_take isl_printer *p,
2838 __isl_keep isl_pw_qpolynomial *pwqp);
2840 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2841 __isl_take isl_printer *p,
2842 __isl_keep isl_union_pw_qpolynomial *upwqp);
2844 The output format of the printer
2845 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2846 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2848 In case of printing in C<ISL_FORMAT_C>, the user may want
2849 to set the names of all dimensions
2851 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2852 __isl_take isl_qpolynomial *qp,
2853 enum isl_dim_type type, unsigned pos,
2855 __isl_give isl_pw_qpolynomial *
2856 isl_pw_qpolynomial_set_dim_name(
2857 __isl_take isl_pw_qpolynomial *pwqp,
2858 enum isl_dim_type type, unsigned pos,
2861 =head3 Creating New (Piecewise) Quasipolynomials
2863 Some simple quasipolynomials can be created using the following functions.
2864 More complicated quasipolynomials can be created by applying
2865 operations such as addition and multiplication
2866 on the resulting quasipolynomials
2868 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2869 __isl_take isl_dim *dim);
2870 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2871 __isl_take isl_dim *dim);
2872 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2873 __isl_take isl_dim *dim);
2874 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2875 __isl_take isl_dim *dim);
2876 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2877 __isl_take isl_dim *dim);
2878 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2879 __isl_take isl_dim *dim,
2880 const isl_int n, const isl_int d);
2881 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2882 __isl_take isl_div *div);
2883 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2884 __isl_take isl_dim *dim,
2885 enum isl_dim_type type, unsigned pos);
2886 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2887 __isl_take isl_aff *aff);
2889 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2890 with a single cell can be created using the following functions.
2891 Multiple of these single cell piecewise quasipolynomials can
2892 be combined to create more complicated piecewise quasipolynomials.
2894 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2895 __isl_take isl_dim *dim);
2896 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2897 __isl_take isl_set *set,
2898 __isl_take isl_qpolynomial *qp);
2899 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2900 __isl_take isl_qpolynomial *qp);
2901 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2902 __isl_take isl_pw_aff *pwaff);
2904 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2905 __isl_take isl_dim *dim);
2906 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2907 __isl_take isl_pw_qpolynomial *pwqp);
2908 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2909 __isl_take isl_union_pw_qpolynomial *upwqp,
2910 __isl_take isl_pw_qpolynomial *pwqp);
2912 Quasipolynomials can be copied and freed again using the following
2915 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2916 __isl_keep isl_qpolynomial *qp);
2917 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2919 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2920 __isl_keep isl_pw_qpolynomial *pwqp);
2921 void *isl_pw_qpolynomial_free(
2922 __isl_take isl_pw_qpolynomial *pwqp);
2924 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2925 __isl_keep isl_union_pw_qpolynomial *upwqp);
2926 void isl_union_pw_qpolynomial_free(
2927 __isl_take isl_union_pw_qpolynomial *upwqp);
2929 =head3 Inspecting (Piecewise) Quasipolynomials
2931 To iterate over all piecewise quasipolynomials in a union
2932 piecewise quasipolynomial, use the following function
2934 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2935 __isl_keep isl_union_pw_qpolynomial *upwqp,
2936 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2939 To extract the piecewise quasipolynomial from a union with a given dimension
2942 __isl_give isl_pw_qpolynomial *
2943 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2944 __isl_keep isl_union_pw_qpolynomial *upwqp,
2945 __isl_take isl_dim *dim);
2947 To iterate over the cells in a piecewise quasipolynomial,
2948 use either of the following two functions
2950 int isl_pw_qpolynomial_foreach_piece(
2951 __isl_keep isl_pw_qpolynomial *pwqp,
2952 int (*fn)(__isl_take isl_set *set,
2953 __isl_take isl_qpolynomial *qp,
2954 void *user), void *user);
2955 int isl_pw_qpolynomial_foreach_lifted_piece(
2956 __isl_keep isl_pw_qpolynomial *pwqp,
2957 int (*fn)(__isl_take isl_set *set,
2958 __isl_take isl_qpolynomial *qp,
2959 void *user), void *user);
2961 As usual, the function C<fn> should return C<0> on success
2962 and C<-1> on failure. The difference between
2963 C<isl_pw_qpolynomial_foreach_piece> and
2964 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2965 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2966 compute unique representations for all existentially quantified
2967 variables and then turn these existentially quantified variables
2968 into extra set variables, adapting the associated quasipolynomial
2969 accordingly. This means that the C<set> passed to C<fn>
2970 will not have any existentially quantified variables, but that
2971 the dimensions of the sets may be different for different
2972 invocations of C<fn>.
2974 To iterate over all terms in a quasipolynomial,
2977 int isl_qpolynomial_foreach_term(
2978 __isl_keep isl_qpolynomial *qp,
2979 int (*fn)(__isl_take isl_term *term,
2980 void *user), void *user);
2982 The terms themselves can be inspected and freed using
2985 unsigned isl_term_dim(__isl_keep isl_term *term,
2986 enum isl_dim_type type);
2987 void isl_term_get_num(__isl_keep isl_term *term,
2989 void isl_term_get_den(__isl_keep isl_term *term,
2991 int isl_term_get_exp(__isl_keep isl_term *term,
2992 enum isl_dim_type type, unsigned pos);
2993 __isl_give isl_div *isl_term_get_div(
2994 __isl_keep isl_term *term, unsigned pos);
2995 void isl_term_free(__isl_take isl_term *term);
2997 Each term is a product of parameters, set variables and
2998 integer divisions. The function C<isl_term_get_exp>
2999 returns the exponent of a given dimensions in the given term.
3000 The C<isl_int>s in the arguments of C<isl_term_get_num>
3001 and C<isl_term_get_den> need to have been initialized
3002 using C<isl_int_init> before calling these functions.
3004 =head3 Properties of (Piecewise) Quasipolynomials
3006 To check whether a quasipolynomial is actually a constant,
3007 use the following function.
3009 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3010 isl_int *n, isl_int *d);
3012 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3013 then the numerator and denominator of the constant
3014 are returned in C<*n> and C<*d>, respectively.
3016 =head3 Operations on (Piecewise) Quasipolynomials
3018 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3019 __isl_take isl_qpolynomial *qp, isl_int v);
3020 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3021 __isl_take isl_qpolynomial *qp);
3022 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3023 __isl_take isl_qpolynomial *qp1,
3024 __isl_take isl_qpolynomial *qp2);
3025 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3026 __isl_take isl_qpolynomial *qp1,
3027 __isl_take isl_qpolynomial *qp2);
3028 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3029 __isl_take isl_qpolynomial *qp1,
3030 __isl_take isl_qpolynomial *qp2);
3031 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3032 __isl_take isl_qpolynomial *qp, unsigned exponent);
3034 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3035 __isl_take isl_pw_qpolynomial *pwqp1,
3036 __isl_take isl_pw_qpolynomial *pwqp2);
3037 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3038 __isl_take isl_pw_qpolynomial *pwqp1,
3039 __isl_take isl_pw_qpolynomial *pwqp2);
3040 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3041 __isl_take isl_pw_qpolynomial *pwqp1,
3042 __isl_take isl_pw_qpolynomial *pwqp2);
3043 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3044 __isl_take isl_pw_qpolynomial *pwqp);
3045 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3046 __isl_take isl_pw_qpolynomial *pwqp1,
3047 __isl_take isl_pw_qpolynomial *pwqp2);
3048 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3049 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3051 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3052 __isl_take isl_union_pw_qpolynomial *upwqp1,
3053 __isl_take isl_union_pw_qpolynomial *upwqp2);
3054 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3055 __isl_take isl_union_pw_qpolynomial *upwqp1,
3056 __isl_take isl_union_pw_qpolynomial *upwqp2);
3057 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3058 __isl_take isl_union_pw_qpolynomial *upwqp1,
3059 __isl_take isl_union_pw_qpolynomial *upwqp2);
3061 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3062 __isl_take isl_pw_qpolynomial *pwqp,
3063 __isl_take isl_point *pnt);
3065 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3066 __isl_take isl_union_pw_qpolynomial *upwqp,
3067 __isl_take isl_point *pnt);
3069 __isl_give isl_set *isl_pw_qpolynomial_domain(
3070 __isl_take isl_pw_qpolynomial *pwqp);
3071 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3072 __isl_take isl_pw_qpolynomial *pwpq,
3073 __isl_take isl_set *set);
3075 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3076 __isl_take isl_union_pw_qpolynomial *upwqp);
3077 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3078 __isl_take isl_union_pw_qpolynomial *upwpq,
3079 __isl_take isl_union_set *uset);
3081 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3082 __isl_take isl_qpolynomial *qp,
3083 __isl_take isl_dim *model);
3085 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3086 __isl_take isl_union_pw_qpolynomial *upwqp);
3088 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3089 __isl_take isl_qpolynomial *qp,
3090 __isl_take isl_set *context);
3092 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3093 __isl_take isl_pw_qpolynomial *pwqp,
3094 __isl_take isl_set *context);
3096 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3097 __isl_take isl_union_pw_qpolynomial *upwqp,
3098 __isl_take isl_union_set *context);
3100 The gist operation applies the gist operation to each of
3101 the cells in the domain of the input piecewise quasipolynomial.
3102 The context is also exploited
3103 to simplify the quasipolynomials associated to each cell.
3105 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3106 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3107 __isl_give isl_union_pw_qpolynomial *
3108 isl_union_pw_qpolynomial_to_polynomial(
3109 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3111 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3112 the polynomial will be an overapproximation. If C<sign> is negative,
3113 it will be an underapproximation. If C<sign> is zero, the approximation
3114 will lie somewhere in between.
3116 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3118 A piecewise quasipolynomial reduction is a piecewise
3119 reduction (or fold) of quasipolynomials.
3120 In particular, the reduction can be maximum or a minimum.
3121 The objects are mainly used to represent the result of
3122 an upper or lower bound on a quasipolynomial over its domain,
3123 i.e., as the result of the following function.
3125 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3126 __isl_take isl_pw_qpolynomial *pwqp,
3127 enum isl_fold type, int *tight);
3129 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3130 __isl_take isl_union_pw_qpolynomial *upwqp,
3131 enum isl_fold type, int *tight);
3133 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3134 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3135 is the returned bound is known be tight, i.e., for each value
3136 of the parameters there is at least
3137 one element in the domain that reaches the bound.
3138 If the domain of C<pwqp> is not wrapping, then the bound is computed
3139 over all elements in that domain and the result has a purely parametric
3140 domain. If the domain of C<pwqp> is wrapping, then the bound is
3141 computed over the range of the wrapped relation. The domain of the
3142 wrapped relation becomes the domain of the result.
3144 A (piecewise) quasipolynomial reduction can be copied or freed using the
3145 following functions.
3147 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3148 __isl_keep isl_qpolynomial_fold *fold);
3149 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3150 __isl_keep isl_pw_qpolynomial_fold *pwf);
3151 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3152 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3153 void isl_qpolynomial_fold_free(
3154 __isl_take isl_qpolynomial_fold *fold);
3155 void *isl_pw_qpolynomial_fold_free(
3156 __isl_take isl_pw_qpolynomial_fold *pwf);
3157 void isl_union_pw_qpolynomial_fold_free(
3158 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3160 =head3 Printing Piecewise Quasipolynomial Reductions
3162 Piecewise quasipolynomial reductions can be printed
3163 using the following function.
3165 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3166 __isl_take isl_printer *p,
3167 __isl_keep isl_pw_qpolynomial_fold *pwf);
3168 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3169 __isl_take isl_printer *p,
3170 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3172 For C<isl_printer_print_pw_qpolynomial_fold>,
3173 output format of the printer
3174 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3175 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3176 output format of the printer
3177 needs to be set to C<ISL_FORMAT_ISL>.
3178 In case of printing in C<ISL_FORMAT_C>, the user may want
3179 to set the names of all dimensions
3181 __isl_give isl_pw_qpolynomial_fold *
3182 isl_pw_qpolynomial_fold_set_dim_name(
3183 __isl_take isl_pw_qpolynomial_fold *pwf,
3184 enum isl_dim_type type, unsigned pos,
3187 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3189 To iterate over all piecewise quasipolynomial reductions in a union
3190 piecewise quasipolynomial reduction, use the following function
3192 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3193 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3194 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3195 void *user), void *user);
3197 To iterate over the cells in a piecewise quasipolynomial reduction,
3198 use either of the following two functions
3200 int isl_pw_qpolynomial_fold_foreach_piece(
3201 __isl_keep isl_pw_qpolynomial_fold *pwf,
3202 int (*fn)(__isl_take isl_set *set,
3203 __isl_take isl_qpolynomial_fold *fold,
3204 void *user), void *user);
3205 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3206 __isl_keep isl_pw_qpolynomial_fold *pwf,
3207 int (*fn)(__isl_take isl_set *set,
3208 __isl_take isl_qpolynomial_fold *fold,
3209 void *user), void *user);
3211 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3212 of the difference between these two functions.
3214 To iterate over all quasipolynomials in a reduction, use
3216 int isl_qpolynomial_fold_foreach_qpolynomial(
3217 __isl_keep isl_qpolynomial_fold *fold,
3218 int (*fn)(__isl_take isl_qpolynomial *qp,
3219 void *user), void *user);
3221 =head3 Operations on Piecewise Quasipolynomial Reductions
3223 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3224 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3226 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3227 __isl_take isl_pw_qpolynomial_fold *pwf1,
3228 __isl_take isl_pw_qpolynomial_fold *pwf2);
3230 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3231 __isl_take isl_pw_qpolynomial_fold *pwf1,
3232 __isl_take isl_pw_qpolynomial_fold *pwf2);
3234 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3235 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3236 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3238 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3239 __isl_take isl_pw_qpolynomial_fold *pwf,
3240 __isl_take isl_point *pnt);
3242 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3243 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3244 __isl_take isl_point *pnt);
3246 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3247 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3248 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3249 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3250 __isl_take isl_union_set *uset);
3252 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3253 __isl_take isl_pw_qpolynomial_fold *pwf);
3255 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3256 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3258 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3259 __isl_take isl_pw_qpolynomial_fold *pwf,
3260 __isl_take isl_set *context);
3262 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3263 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3264 __isl_take isl_union_set *context);
3266 The gist operation applies the gist operation to each of
3267 the cells in the domain of the input piecewise quasipolynomial reduction.
3268 In future, the operation will also exploit the context
3269 to simplify the quasipolynomial reductions associated to each cell.
3271 __isl_give isl_pw_qpolynomial_fold *
3272 isl_set_apply_pw_qpolynomial_fold(
3273 __isl_take isl_set *set,
3274 __isl_take isl_pw_qpolynomial_fold *pwf,
3276 __isl_give isl_pw_qpolynomial_fold *
3277 isl_map_apply_pw_qpolynomial_fold(
3278 __isl_take isl_map *map,
3279 __isl_take isl_pw_qpolynomial_fold *pwf,
3281 __isl_give isl_union_pw_qpolynomial_fold *
3282 isl_union_set_apply_union_pw_qpolynomial_fold(
3283 __isl_take isl_union_set *uset,
3284 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3286 __isl_give isl_union_pw_qpolynomial_fold *
3287 isl_union_map_apply_union_pw_qpolynomial_fold(
3288 __isl_take isl_union_map *umap,
3289 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3292 The functions taking a map
3293 compose the given map with the given piecewise quasipolynomial reduction.
3294 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3295 over all elements in the intersection of the range of the map
3296 and the domain of the piecewise quasipolynomial reduction
3297 as a function of an element in the domain of the map.
3298 The functions taking a set compute a bound over all elements in the
3299 intersection of the set and the domain of the
3300 piecewise quasipolynomial reduction.
3302 =head2 Dependence Analysis
3304 C<isl> contains specialized functionality for performing
3305 array dataflow analysis. That is, given a I<sink> access relation
3306 and a collection of possible I<source> access relations,
3307 C<isl> can compute relations that describe
3308 for each iteration of the sink access, which iteration
3309 of which of the source access relations was the last
3310 to access the same data element before the given iteration
3312 To compute standard flow dependences, the sink should be
3313 a read, while the sources should be writes.
3314 If any of the source accesses are marked as being I<may>
3315 accesses, then there will be a dependence to the last
3316 I<must> access B<and> to any I<may> access that follows
3317 this last I<must> access.
3318 In particular, if I<all> sources are I<may> accesses,
3319 then memory based dependence analysis is performed.
3320 If, on the other hand, all sources are I<must> accesses,
3321 then value based dependence analysis is performed.
3323 #include <isl/flow.h>
3325 typedef int (*isl_access_level_before)(void *first, void *second);
3327 __isl_give isl_access_info *isl_access_info_alloc(
3328 __isl_take isl_map *sink,
3329 void *sink_user, isl_access_level_before fn,
3331 __isl_give isl_access_info *isl_access_info_add_source(
3332 __isl_take isl_access_info *acc,
3333 __isl_take isl_map *source, int must,
3335 void isl_access_info_free(__isl_take isl_access_info *acc);
3337 __isl_give isl_flow *isl_access_info_compute_flow(
3338 __isl_take isl_access_info *acc);
3340 int isl_flow_foreach(__isl_keep isl_flow *deps,
3341 int (*fn)(__isl_take isl_map *dep, int must,
3342 void *dep_user, void *user),
3344 __isl_give isl_map *isl_flow_get_no_source(
3345 __isl_keep isl_flow *deps, int must);
3346 void isl_flow_free(__isl_take isl_flow *deps);
3348 The function C<isl_access_info_compute_flow> performs the actual
3349 dependence analysis. The other functions are used to construct
3350 the input for this function or to read off the output.
3352 The input is collected in an C<isl_access_info>, which can
3353 be created through a call to C<isl_access_info_alloc>.
3354 The arguments to this functions are the sink access relation
3355 C<sink>, a token C<sink_user> used to identify the sink
3356 access to the user, a callback function for specifying the
3357 relative order of source and sink accesses, and the number
3358 of source access relations that will be added.
3359 The callback function has type C<int (*)(void *first, void *second)>.
3360 The function is called with two user supplied tokens identifying
3361 either a source or the sink and it should return the shared nesting
3362 level and the relative order of the two accesses.
3363 In particular, let I<n> be the number of loops shared by
3364 the two accesses. If C<first> precedes C<second> textually,
3365 then the function should return I<2 * n + 1>; otherwise,
3366 it should return I<2 * n>.
3367 The sources can be added to the C<isl_access_info> by performing
3368 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3369 C<must> indicates whether the source is a I<must> access
3370 or a I<may> access. Note that a multi-valued access relation
3371 should only be marked I<must> if every iteration in the domain
3372 of the relation accesses I<all> elements in its image.
3373 The C<source_user> token is again used to identify
3374 the source access. The range of the source access relation
3375 C<source> should have the same dimension as the range
3376 of the sink access relation.
3377 The C<isl_access_info_free> function should usually not be
3378 called explicitly, because it is called implicitly by
3379 C<isl_access_info_compute_flow>.
3381 The result of the dependence analysis is collected in an
3382 C<isl_flow>. There may be elements of
3383 the sink access for which no preceding source access could be
3384 found or for which all preceding sources are I<may> accesses.
3385 The relations containing these elements can be obtained through
3386 calls to C<isl_flow_get_no_source>, the first with C<must> set
3387 and the second with C<must> unset.
3388 In the case of standard flow dependence analysis,
3389 with the sink a read and the sources I<must> writes,
3390 the first relation corresponds to the reads from uninitialized
3391 array elements and the second relation is empty.
3392 The actual flow dependences can be extracted using
3393 C<isl_flow_foreach>. This function will call the user-specified
3394 callback function C<fn> for each B<non-empty> dependence between
3395 a source and the sink. The callback function is called
3396 with four arguments, the actual flow dependence relation
3397 mapping source iterations to sink iterations, a boolean that
3398 indicates whether it is a I<must> or I<may> dependence, a token
3399 identifying the source and an additional C<void *> with value
3400 equal to the third argument of the C<isl_flow_foreach> call.
3401 A dependence is marked I<must> if it originates from a I<must>
3402 source and if it is not followed by any I<may> sources.
3404 After finishing with an C<isl_flow>, the user should call
3405 C<isl_flow_free> to free all associated memory.
3407 A higher-level interface to dependence analysis is provided
3408 by the following function.
3410 #include <isl/flow.h>
3412 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3413 __isl_take isl_union_map *must_source,
3414 __isl_take isl_union_map *may_source,
3415 __isl_take isl_union_map *schedule,
3416 __isl_give isl_union_map **must_dep,
3417 __isl_give isl_union_map **may_dep,
3418 __isl_give isl_union_map **must_no_source,
3419 __isl_give isl_union_map **may_no_source);
3421 The arrays are identified by the tuple names of the ranges
3422 of the accesses. The iteration domains by the tuple names
3423 of the domains of the accesses and of the schedule.
3424 The relative order of the iteration domains is given by the
3425 schedule. The relations returned through C<must_no_source>
3426 and C<may_no_source> are subsets of C<sink>.
3427 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3428 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3429 any of the other arguments is treated as an error.
3433 B<The functionality described in this section is fairly new
3434 and may be subject to change.>
3436 The following function can be used to compute a schedule
3437 for a union of domains. The generated schedule respects
3438 all C<validity> dependences. That is, all dependence distances
3439 over these dependences in the scheduled space are lexicographically
3440 positive. The generated schedule schedule also tries to minimize
3441 the dependence distances over C<proximity> dependences.
3442 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3443 for groups of domains where the dependence distances have only
3444 non-negative values.
3445 The algorithm used to construct the schedule is similar to that
3448 #include <isl/schedule.h>
3449 __isl_give isl_schedule *isl_union_set_compute_schedule(
3450 __isl_take isl_union_set *domain,
3451 __isl_take isl_union_map *validity,
3452 __isl_take isl_union_map *proximity);
3453 void *isl_schedule_free(__isl_take isl_schedule *sched);
3455 A mapping from the domains to the scheduled space can be obtained
3456 from an C<isl_schedule> using the following function.
3458 __isl_give isl_union_map *isl_schedule_get_map(
3459 __isl_keep isl_schedule *sched);
3461 A representation of the schedule can be printed using
3463 __isl_give isl_printer *isl_printer_print_schedule(
3464 __isl_take isl_printer *p,
3465 __isl_keep isl_schedule *schedule);
3467 A representation of the schedule as a forest of bands can be obtained
3468 using the following function.
3470 __isl_give isl_band_list *isl_schedule_get_band_forest(
3471 __isl_keep isl_schedule *schedule);
3473 The list can be manipulated as explained in L<"Lists">.
3474 The bands inside the list can be copied and freed using the following
3477 #include <isl/band.h>
3478 __isl_give isl_band *isl_band_copy(
3479 __isl_keep isl_band *band);
3480 void *isl_band_free(__isl_take isl_band *band);
3482 Each band contains zero or more scheduling dimensions.
3483 These are referred to as the members of the band.
3484 The section of the schedule that corresponds to the band is
3485 referred to as the partial schedule of the band.
3486 For those nodes that participate in a band, the outer scheduling
3487 dimensions form the prefix schedule, while the inner scheduling
3488 dimensions form the suffix schedule.
3489 That is, if we take a cut of the band forest, then the union of
3490 the concatenations of the prefix, partial and suffix schedules of
3491 each band in the cut is equal to the entire schedule (modulo
3492 some possible padding at the end with zero scheduling dimensions).
3493 The properties of a band can be inspected using the following functions.
3495 #include <isl/band.h>
3496 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3498 int isl_band_has_children(__isl_keep isl_band *band);
3499 __isl_give isl_band_list *isl_band_get_children(
3500 __isl_keep isl_band *band);
3502 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3503 __isl_keep isl_band *band);
3504 __isl_give isl_union_map *isl_band_get_partial_schedule(
3505 __isl_keep isl_band *band);
3506 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3507 __isl_keep isl_band *band);
3509 int isl_band_n_member(__isl_keep isl_band *band);
3510 int isl_band_member_is_zero_distance(
3511 __isl_keep isl_band *band, int pos);
3513 Note that a scheduling dimension is considered to be ``zero
3514 distance'' if it does not carry any proximity dependences
3516 That is, if the dependence distances of the proximity
3517 dependences are all zero in that direction (for fixed
3518 iterations of outer bands).
3520 A representation of the band can be printed using
3522 #include <isl/band.h>
3523 __isl_give isl_printer *isl_printer_print_band(
3524 __isl_take isl_printer *p,
3525 __isl_keep isl_band *band);
3527 =head2 Parametric Vertex Enumeration
3529 The parametric vertex enumeration described in this section
3530 is mainly intended to be used internally and by the C<barvinok>
3533 #include <isl/vertices.h>
3534 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3535 __isl_keep isl_basic_set *bset);
3537 The function C<isl_basic_set_compute_vertices> performs the
3538 actual computation of the parametric vertices and the chamber
3539 decomposition and store the result in an C<isl_vertices> object.
3540 This information can be queried by either iterating over all
3541 the vertices or iterating over all the chambers or cells
3542 and then iterating over all vertices that are active on the chamber.
3544 int isl_vertices_foreach_vertex(
3545 __isl_keep isl_vertices *vertices,
3546 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3549 int isl_vertices_foreach_cell(
3550 __isl_keep isl_vertices *vertices,
3551 int (*fn)(__isl_take isl_cell *cell, void *user),
3553 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3554 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3557 Other operations that can be performed on an C<isl_vertices> object are
3560 isl_ctx *isl_vertices_get_ctx(
3561 __isl_keep isl_vertices *vertices);
3562 int isl_vertices_get_n_vertices(
3563 __isl_keep isl_vertices *vertices);
3564 void isl_vertices_free(__isl_take isl_vertices *vertices);
3566 Vertices can be inspected and destroyed using the following functions.
3568 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3569 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3570 __isl_give isl_basic_set *isl_vertex_get_domain(
3571 __isl_keep isl_vertex *vertex);
3572 __isl_give isl_basic_set *isl_vertex_get_expr(
3573 __isl_keep isl_vertex *vertex);
3574 void isl_vertex_free(__isl_take isl_vertex *vertex);
3576 C<isl_vertex_get_expr> returns a singleton parametric set describing
3577 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3579 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3580 B<rational> basic sets, so they should mainly be used for inspection
3581 and should not be mixed with integer sets.
3583 Chambers can be inspected and destroyed using the following functions.
3585 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3586 __isl_give isl_basic_set *isl_cell_get_domain(
3587 __isl_keep isl_cell *cell);
3588 void isl_cell_free(__isl_take isl_cell *cell);
3592 Although C<isl> is mainly meant to be used as a library,
3593 it also contains some basic applications that use some
3594 of the functionality of C<isl>.
3595 The input may be specified in either the L<isl format>
3596 or the L<PolyLib format>.
3598 =head2 C<isl_polyhedron_sample>
3600 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3601 an integer element of the polyhedron, if there is any.
3602 The first column in the output is the denominator and is always
3603 equal to 1. If the polyhedron contains no integer points,
3604 then a vector of length zero is printed.
3608 C<isl_pip> takes the same input as the C<example> program
3609 from the C<piplib> distribution, i.e., a set of constraints
3610 on the parameters, a line containing only -1 and finally a set
3611 of constraints on a parametric polyhedron.
3612 The coefficients of the parameters appear in the last columns
3613 (but before the final constant column).
3614 The output is the lexicographic minimum of the parametric polyhedron.
3615 As C<isl> currently does not have its own output format, the output
3616 is just a dump of the internal state.
3618 =head2 C<isl_polyhedron_minimize>
3620 C<isl_polyhedron_minimize> computes the minimum of some linear
3621 or affine objective function over the integer points in a polyhedron.
3622 If an affine objective function
3623 is given, then the constant should appear in the last column.
3625 =head2 C<isl_polytope_scan>
3627 Given a polytope, C<isl_polytope_scan> prints
3628 all integer points in the polytope.