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 documents 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 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 __isl_give isl_id *isl_dim_get_dim_id(
543 __isl_keep isl_dim *dim,
544 enum isl_dim_type type, unsigned pos);
545 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
546 enum isl_dim_type type, unsigned pos,
547 __isl_keep const char *name);
548 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
549 enum isl_dim_type type, unsigned pos);
551 Note that C<isl_dim_get_name> returns a pointer to some internal
552 data structure, so the result can only be used while the
553 corresponding C<isl_dim> is alive.
554 Also note that every function that operates on two sets or relations
555 requires that both arguments have the same parameters. This also
556 means that if one of the arguments has named parameters, then the
557 other needs to have named parameters too and the names need to match.
558 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
559 arguments may have different parameters (as long as they are named),
560 in which case the result will have as parameters the union of the parameters of
563 Given the identifier of a dimension (typically a parameter),
564 its position can be obtained from the following function.
567 int isl_dim_find_dim_by_id(__isl_keep isl_dim *dim,
568 enum isl_dim_type type, __isl_keep isl_id *id);
570 The identifiers or names of entire spaces may be set or read off
571 using the following functions.
574 __isl_give isl_dim *isl_dim_set_tuple_id(
575 __isl_take isl_dim *dim,
576 enum isl_dim_type type, __isl_take isl_id *id);
577 __isl_give isl_dim *isl_dim_reset_tuple_id(
578 __isl_take isl_dim *dim, enum isl_dim_type type);
579 __isl_give isl_id *isl_dim_get_tuple_id(
580 __isl_keep isl_dim *dim, enum isl_dim_type type);
581 __isl_give isl_dim *isl_dim_set_tuple_name(
582 __isl_take isl_dim *dim,
583 enum isl_dim_type type, const char *s);
584 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
585 enum isl_dim_type type);
587 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
588 or C<isl_dim_set>. As with C<isl_dim_get_name>,
589 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
591 Binary operations require the corresponding spaces of their arguments
592 to have the same name.
594 Spaces can be nested. In particular, the domain of a set or
595 the domain or range of a relation can be a nested relation.
596 The following functions can be used to construct and deconstruct
597 such nested dimension specifications.
600 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
601 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
602 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
604 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
605 be the dimension specification of a set, while that of
606 C<isl_dim_wrap> should be the dimension specification of a relation.
607 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
608 of a relation, while that of C<isl_dim_wrap> is the dimension specification
611 Dimension specifications can be created from other dimension
612 specifications using the following functions.
614 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
615 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
616 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
617 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
618 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
619 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
620 __isl_take isl_dim *right);
621 __isl_give isl_dim *isl_dim_align_params(
622 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
623 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
624 enum isl_dim_type type, unsigned pos, unsigned n);
625 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
626 enum isl_dim_type type, unsigned n);
627 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
628 enum isl_dim_type type, unsigned first, unsigned n);
629 __isl_give isl_dim *isl_dim_map_from_set(
630 __isl_take isl_dim *dim);
631 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
633 Note that if dimensions are added or removed from a space, then
634 the name and the internal structure are lost.
638 A local space is essentially a dimension specification with
639 zero or more existentially quantified variables.
640 The local space of a basic set or relation can be obtained
641 using the following functions.
644 __isl_give isl_local_space *isl_basic_set_get_local_space(
645 __isl_keep isl_basic_set *bset);
648 __isl_give isl_local_space *isl_basic_map_get_local_space(
649 __isl_keep isl_basic_map *bmap);
651 A new local space can be created from a dimension specification using
653 #include <isl/local_space.h>
654 __isl_give isl_local_space *isl_local_space_from_dim(
655 __isl_take isl_dim *dim);
657 They can be inspected, copied and freed using the following functions.
659 #include <isl/local_space.h>
660 isl_ctx *isl_local_space_get_ctx(
661 __isl_keep isl_local_space *ls);
662 int isl_local_space_dim(__isl_keep isl_local_space *ls,
663 enum isl_dim_type type);
664 const char *isl_local_space_get_dim_name(
665 __isl_keep isl_local_space *ls,
666 enum isl_dim_type type, unsigned pos);
667 __isl_give isl_local_space *isl_local_space_set_dim_name(
668 __isl_take isl_local_space *ls,
669 enum isl_dim_type type, unsigned pos, const char *s);
670 __isl_give isl_dim *isl_local_space_get_dim(
671 __isl_keep isl_local_space *ls);
672 __isl_give isl_div *isl_local_space_get_div(
673 __isl_keep isl_local_space *ls, int pos);
674 __isl_give isl_local_space *isl_local_space_copy(
675 __isl_keep isl_local_space *ls);
676 void *isl_local_space_free(__isl_take isl_local_space *ls);
678 Two local spaces can be compared using
680 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
681 __isl_keep isl_local_space *ls2);
683 Local spaces can be created from other local spaces
684 using the following functions.
686 __isl_give isl_local_space *isl_local_space_from_domain(
687 __isl_take isl_local_space *ls);
688 __isl_give isl_local_space *isl_local_space_add_dims(
689 __isl_take isl_local_space *ls,
690 enum isl_dim_type type, unsigned n);
691 __isl_give isl_local_space *isl_local_space_insert_dims(
692 __isl_take isl_local_space *ls,
693 enum isl_dim_type type, unsigned first, unsigned n);
694 __isl_give isl_local_space *isl_local_space_drop_dims(
695 __isl_take isl_local_space *ls,
696 enum isl_dim_type type, unsigned first, unsigned n);
698 =head2 Input and Output
700 C<isl> supports its own input/output format, which is similar
701 to the C<Omega> format, but also supports the C<PolyLib> format
706 The C<isl> format is similar to that of C<Omega>, but has a different
707 syntax for describing the parameters and allows for the definition
708 of an existentially quantified variable as the integer division
709 of an affine expression.
710 For example, the set of integers C<i> between C<0> and C<n>
711 such that C<i % 10 <= 6> can be described as
713 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
716 A set or relation can have several disjuncts, separated
717 by the keyword C<or>. Each disjunct is either a conjunction
718 of constraints or a projection (C<exists>) of a conjunction
719 of constraints. The constraints are separated by the keyword
722 =head3 C<PolyLib> format
724 If the represented set is a union, then the first line
725 contains a single number representing the number of disjuncts.
726 Otherwise, a line containing the number C<1> is optional.
728 Each disjunct is represented by a matrix of constraints.
729 The first line contains two numbers representing
730 the number of rows and columns,
731 where the number of rows is equal to the number of constraints
732 and the number of columns is equal to two plus the number of variables.
733 The following lines contain the actual rows of the constraint matrix.
734 In each row, the first column indicates whether the constraint
735 is an equality (C<0>) or inequality (C<1>). The final column
736 corresponds to the constant term.
738 If the set is parametric, then the coefficients of the parameters
739 appear in the last columns before the constant column.
740 The coefficients of any existentially quantified variables appear
741 between those of the set variables and those of the parameters.
743 =head3 Extended C<PolyLib> format
745 The extended C<PolyLib> format is nearly identical to the
746 C<PolyLib> format. The only difference is that the line
747 containing the number of rows and columns of a constraint matrix
748 also contains four additional numbers:
749 the number of output dimensions, the number of input dimensions,
750 the number of local dimensions (i.e., the number of existentially
751 quantified variables) and the number of parameters.
752 For sets, the number of ``output'' dimensions is equal
753 to the number of set dimensions, while the number of ``input''
759 __isl_give isl_basic_set *isl_basic_set_read_from_file(
760 isl_ctx *ctx, FILE *input, int nparam);
761 __isl_give isl_basic_set *isl_basic_set_read_from_str(
762 isl_ctx *ctx, const char *str, int nparam);
763 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
764 FILE *input, int nparam);
765 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
766 const char *str, int nparam);
769 __isl_give isl_basic_map *isl_basic_map_read_from_file(
770 isl_ctx *ctx, FILE *input, int nparam);
771 __isl_give isl_basic_map *isl_basic_map_read_from_str(
772 isl_ctx *ctx, const char *str, int nparam);
773 __isl_give isl_map *isl_map_read_from_file(
774 struct isl_ctx *ctx, FILE *input, int nparam);
775 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
776 const char *str, int nparam);
778 #include <isl/union_set.h>
779 __isl_give isl_union_set *isl_union_set_read_from_file(
780 isl_ctx *ctx, FILE *input);
781 __isl_give isl_union_set *isl_union_set_read_from_str(
782 struct isl_ctx *ctx, const char *str);
784 #include <isl/union_map.h>
785 __isl_give isl_union_map *isl_union_map_read_from_file(
786 isl_ctx *ctx, FILE *input);
787 __isl_give isl_union_map *isl_union_map_read_from_str(
788 struct isl_ctx *ctx, const char *str);
790 The input format is autodetected and may be either the C<PolyLib> format
791 or the C<isl> format.
792 C<nparam> specifies how many of the final columns in
793 the C<PolyLib> format correspond to parameters.
794 If input is given in the C<isl> format, then the number
795 of parameters needs to be equal to C<nparam>.
796 If C<nparam> is negative, then any number of parameters
797 is accepted in the C<isl> format and zero parameters
798 are assumed in the C<PolyLib> format.
802 Before anything can be printed, an C<isl_printer> needs to
805 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
807 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
808 void isl_printer_free(__isl_take isl_printer *printer);
809 __isl_give char *isl_printer_get_str(
810 __isl_keep isl_printer *printer);
812 The behavior of the printer can be modified in various ways
814 __isl_give isl_printer *isl_printer_set_output_format(
815 __isl_take isl_printer *p, int output_format);
816 __isl_give isl_printer *isl_printer_set_indent(
817 __isl_take isl_printer *p, int indent);
818 __isl_give isl_printer *isl_printer_indent(
819 __isl_take isl_printer *p, int indent);
820 __isl_give isl_printer *isl_printer_set_prefix(
821 __isl_take isl_printer *p, const char *prefix);
822 __isl_give isl_printer *isl_printer_set_suffix(
823 __isl_take isl_printer *p, const char *suffix);
825 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
826 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
827 and defaults to C<ISL_FORMAT_ISL>.
828 Each line in the output is indented by C<indent> (set by
829 C<isl_printer_set_indent>) spaces
830 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
831 In the C<PolyLib> format output,
832 the coefficients of the existentially quantified variables
833 appear between those of the set variables and those
835 The function C<isl_printer_indent> increases the indentation
836 by the specified amount (which may be negative).
838 To actually print something, use
841 __isl_give isl_printer *isl_printer_print_basic_set(
842 __isl_take isl_printer *printer,
843 __isl_keep isl_basic_set *bset);
844 __isl_give isl_printer *isl_printer_print_set(
845 __isl_take isl_printer *printer,
846 __isl_keep isl_set *set);
849 __isl_give isl_printer *isl_printer_print_basic_map(
850 __isl_take isl_printer *printer,
851 __isl_keep isl_basic_map *bmap);
852 __isl_give isl_printer *isl_printer_print_map(
853 __isl_take isl_printer *printer,
854 __isl_keep isl_map *map);
856 #include <isl/union_set.h>
857 __isl_give isl_printer *isl_printer_print_union_set(
858 __isl_take isl_printer *p,
859 __isl_keep isl_union_set *uset);
861 #include <isl/union_map.h>
862 __isl_give isl_printer *isl_printer_print_union_map(
863 __isl_take isl_printer *p,
864 __isl_keep isl_union_map *umap);
866 When called on a file printer, the following function flushes
867 the file. When called on a string printer, the buffer is cleared.
869 __isl_give isl_printer *isl_printer_flush(
870 __isl_take isl_printer *p);
872 =head2 Creating New Sets and Relations
874 C<isl> has functions for creating some standard sets and relations.
878 =item * Empty sets and relations
880 __isl_give isl_basic_set *isl_basic_set_empty(
881 __isl_take isl_dim *dim);
882 __isl_give isl_basic_map *isl_basic_map_empty(
883 __isl_take isl_dim *dim);
884 __isl_give isl_set *isl_set_empty(
885 __isl_take isl_dim *dim);
886 __isl_give isl_map *isl_map_empty(
887 __isl_take isl_dim *dim);
888 __isl_give isl_union_set *isl_union_set_empty(
889 __isl_take isl_dim *dim);
890 __isl_give isl_union_map *isl_union_map_empty(
891 __isl_take isl_dim *dim);
893 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
894 is only used to specify the parameters.
896 =item * Universe sets and relations
898 __isl_give isl_basic_set *isl_basic_set_universe(
899 __isl_take isl_dim *dim);
900 __isl_give isl_basic_map *isl_basic_map_universe(
901 __isl_take isl_dim *dim);
902 __isl_give isl_set *isl_set_universe(
903 __isl_take isl_dim *dim);
904 __isl_give isl_map *isl_map_universe(
905 __isl_take isl_dim *dim);
906 __isl_give isl_union_set *isl_union_set_universe(
907 __isl_take isl_union_set *uset);
908 __isl_give isl_union_map *isl_union_map_universe(
909 __isl_take isl_union_map *umap);
911 The sets and relations constructed by the functions above
912 contain all integer values, while those constructed by the
913 functions below only contain non-negative values.
915 __isl_give isl_basic_set *isl_basic_set_nat_universe(
916 __isl_take isl_dim *dim);
917 __isl_give isl_basic_map *isl_basic_map_nat_universe(
918 __isl_take isl_dim *dim);
919 __isl_give isl_set *isl_set_nat_universe(
920 __isl_take isl_dim *dim);
921 __isl_give isl_map *isl_map_nat_universe(
922 __isl_take isl_dim *dim);
924 =item * Identity relations
926 __isl_give isl_basic_map *isl_basic_map_identity(
927 __isl_take isl_dim *dim);
928 __isl_give isl_map *isl_map_identity(
929 __isl_take isl_dim *dim);
931 The number of input and output dimensions in C<dim> needs
934 =item * Lexicographic order
936 __isl_give isl_map *isl_map_lex_lt(
937 __isl_take isl_dim *set_dim);
938 __isl_give isl_map *isl_map_lex_le(
939 __isl_take isl_dim *set_dim);
940 __isl_give isl_map *isl_map_lex_gt(
941 __isl_take isl_dim *set_dim);
942 __isl_give isl_map *isl_map_lex_ge(
943 __isl_take isl_dim *set_dim);
944 __isl_give isl_map *isl_map_lex_lt_first(
945 __isl_take isl_dim *dim, unsigned n);
946 __isl_give isl_map *isl_map_lex_le_first(
947 __isl_take isl_dim *dim, unsigned n);
948 __isl_give isl_map *isl_map_lex_gt_first(
949 __isl_take isl_dim *dim, unsigned n);
950 __isl_give isl_map *isl_map_lex_ge_first(
951 __isl_take isl_dim *dim, unsigned n);
953 The first four functions take a dimension specification for a B<set>
954 and return relations that express that the elements in the domain
955 are lexicographically less
956 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
957 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
958 than the elements in the range.
959 The last four functions take a dimension specification for a map
960 and return relations that express that the first C<n> dimensions
961 in the domain are lexicographically less
962 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
963 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
964 than the first C<n> dimensions in the range.
968 A basic set or relation can be converted to a set or relation
969 using the following functions.
971 __isl_give isl_set *isl_set_from_basic_set(
972 __isl_take isl_basic_set *bset);
973 __isl_give isl_map *isl_map_from_basic_map(
974 __isl_take isl_basic_map *bmap);
976 Sets and relations can be converted to union sets and relations
977 using the following functions.
979 __isl_give isl_union_map *isl_union_map_from_map(
980 __isl_take isl_map *map);
981 __isl_give isl_union_set *isl_union_set_from_set(
982 __isl_take isl_set *set);
984 The inverse conversions below can only be used if the input
985 union set or relation is known to contain elements in exactly one
988 __isl_give isl_set *isl_set_from_union_set(
989 __isl_take isl_union_set *uset);
990 __isl_give isl_map *isl_map_from_union_map(
991 __isl_take isl_union_map *umap);
993 Sets and relations can be copied and freed again using the following
996 __isl_give isl_basic_set *isl_basic_set_copy(
997 __isl_keep isl_basic_set *bset);
998 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
999 __isl_give isl_union_set *isl_union_set_copy(
1000 __isl_keep isl_union_set *uset);
1001 __isl_give isl_basic_map *isl_basic_map_copy(
1002 __isl_keep isl_basic_map *bmap);
1003 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1004 __isl_give isl_union_map *isl_union_map_copy(
1005 __isl_keep isl_union_map *umap);
1006 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1007 void isl_set_free(__isl_take isl_set *set);
1008 void *isl_union_set_free(__isl_take isl_union_set *uset);
1009 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1010 void isl_map_free(__isl_take isl_map *map);
1011 void *isl_union_map_free(__isl_take isl_union_map *umap);
1013 Other sets and relations can be constructed by starting
1014 from a universe set or relation, adding equality and/or
1015 inequality constraints and then projecting out the
1016 existentially quantified variables, if any.
1017 Constraints can be constructed, manipulated and
1018 added to (or removed from) (basic) sets and relations
1019 using the following functions.
1021 #include <isl/constraint.h>
1022 __isl_give isl_constraint *isl_equality_alloc(
1023 __isl_take isl_dim *dim);
1024 __isl_give isl_constraint *isl_inequality_alloc(
1025 __isl_take isl_dim *dim);
1026 __isl_give isl_constraint *isl_constraint_set_constant(
1027 __isl_take isl_constraint *constraint, isl_int v);
1028 __isl_give isl_constraint *isl_constraint_set_constant_si(
1029 __isl_take isl_constraint *constraint, int v);
1030 __isl_give isl_constraint *isl_constraint_set_coefficient(
1031 __isl_take isl_constraint *constraint,
1032 enum isl_dim_type type, int pos, isl_int v);
1033 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1034 __isl_take isl_constraint *constraint,
1035 enum isl_dim_type type, int pos, int v);
1036 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1037 __isl_take isl_basic_map *bmap,
1038 __isl_take isl_constraint *constraint);
1039 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1040 __isl_take isl_basic_set *bset,
1041 __isl_take isl_constraint *constraint);
1042 __isl_give isl_map *isl_map_add_constraint(
1043 __isl_take isl_map *map,
1044 __isl_take isl_constraint *constraint);
1045 __isl_give isl_set *isl_set_add_constraint(
1046 __isl_take isl_set *set,
1047 __isl_take isl_constraint *constraint);
1048 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1049 __isl_take isl_basic_set *bset,
1050 __isl_take isl_constraint *constraint);
1052 For example, to create a set containing the even integers
1053 between 10 and 42, you would use the following code.
1056 struct isl_dim *dim;
1057 struct isl_constraint *c;
1058 struct isl_basic_set *bset;
1061 dim = isl_dim_set_alloc(ctx, 0, 2);
1062 bset = isl_basic_set_universe(isl_dim_copy(dim));
1064 c = isl_equality_alloc(isl_dim_copy(dim));
1065 isl_int_set_si(v, -1);
1066 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1067 isl_int_set_si(v, 2);
1068 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1069 bset = isl_basic_set_add_constraint(bset, c);
1071 c = isl_inequality_alloc(isl_dim_copy(dim));
1072 isl_int_set_si(v, -10);
1073 isl_constraint_set_constant(c, v);
1074 isl_int_set_si(v, 1);
1075 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1076 bset = isl_basic_set_add_constraint(bset, c);
1078 c = isl_inequality_alloc(dim);
1079 isl_int_set_si(v, 42);
1080 isl_constraint_set_constant(c, v);
1081 isl_int_set_si(v, -1);
1082 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1083 bset = isl_basic_set_add_constraint(bset, c);
1085 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1091 struct isl_basic_set *bset;
1092 bset = isl_basic_set_read_from_str(ctx,
1093 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1095 A basic set or relation can also be constructed from two matrices
1096 describing the equalities and the inequalities.
1098 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1099 __isl_take isl_dim *dim,
1100 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1101 enum isl_dim_type c1,
1102 enum isl_dim_type c2, enum isl_dim_type c3,
1103 enum isl_dim_type c4);
1104 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1105 __isl_take isl_dim *dim,
1106 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1107 enum isl_dim_type c1,
1108 enum isl_dim_type c2, enum isl_dim_type c3,
1109 enum isl_dim_type c4, enum isl_dim_type c5);
1111 The C<isl_dim_type> arguments indicate the order in which
1112 different kinds of variables appear in the input matrices
1113 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1114 C<isl_dim_set> and C<isl_dim_div> for sets and
1115 of C<isl_dim_cst>, C<isl_dim_param>,
1116 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1118 A (basic) relation can also be constructed from a (piecewise) affine expression
1119 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1121 __isl_give isl_basic_map *isl_basic_map_from_aff(
1122 __isl_take isl_aff *aff);
1123 __isl_give isl_map *isl_map_from_pw_aff(
1124 __isl_take isl_pw_aff *pwaff);
1125 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1126 __isl_take isl_dim *domain_dim,
1127 __isl_take isl_aff_list *list);
1129 The C<domain_dim> argument describes the domain of the resulting
1130 basic relation. It is required because the C<list> may consist
1131 of zero affine expressions.
1133 =head2 Inspecting Sets and Relations
1135 Usually, the user should not have to care about the actual constraints
1136 of the sets and maps, but should instead apply the abstract operations
1137 explained in the following sections.
1138 Occasionally, however, it may be required to inspect the individual
1139 coefficients of the constraints. This section explains how to do so.
1140 In these cases, it may also be useful to have C<isl> compute
1141 an explicit representation of the existentially quantified variables.
1143 __isl_give isl_set *isl_set_compute_divs(
1144 __isl_take isl_set *set);
1145 __isl_give isl_map *isl_map_compute_divs(
1146 __isl_take isl_map *map);
1147 __isl_give isl_union_set *isl_union_set_compute_divs(
1148 __isl_take isl_union_set *uset);
1149 __isl_give isl_union_map *isl_union_map_compute_divs(
1150 __isl_take isl_union_map *umap);
1152 This explicit representation defines the existentially quantified
1153 variables as integer divisions of the other variables, possibly
1154 including earlier existentially quantified variables.
1155 An explicitly represented existentially quantified variable therefore
1156 has a unique value when the values of the other variables are known.
1157 If, furthermore, the same existentials, i.e., existentials
1158 with the same explicit representations, should appear in the
1159 same order in each of the disjuncts of a set or map, then the user should call
1160 either of the following functions.
1162 __isl_give isl_set *isl_set_align_divs(
1163 __isl_take isl_set *set);
1164 __isl_give isl_map *isl_map_align_divs(
1165 __isl_take isl_map *map);
1167 Alternatively, the existentially quantified variables can be removed
1168 using the following functions, which compute an overapproximation.
1170 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1171 __isl_take isl_basic_set *bset);
1172 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1173 __isl_take isl_basic_map *bmap);
1174 __isl_give isl_set *isl_set_remove_divs(
1175 __isl_take isl_set *set);
1176 __isl_give isl_map *isl_map_remove_divs(
1177 __isl_take isl_map *map);
1179 To iterate over all the sets or maps in a union set or map, use
1181 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1182 int (*fn)(__isl_take isl_set *set, void *user),
1184 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1185 int (*fn)(__isl_take isl_map *map, void *user),
1188 The number of sets or maps in a union set or map can be obtained
1191 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1192 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1194 To extract the set or map from a union with a given dimension
1197 __isl_give isl_set *isl_union_set_extract_set(
1198 __isl_keep isl_union_set *uset,
1199 __isl_take isl_dim *dim);
1200 __isl_give isl_map *isl_union_map_extract_map(
1201 __isl_keep isl_union_map *umap,
1202 __isl_take isl_dim *dim);
1204 To iterate over all the basic sets or maps in a set or map, use
1206 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1207 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1209 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1210 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1213 The callback function C<fn> should return 0 if successful and
1214 -1 if an error occurs. In the latter case, or if any other error
1215 occurs, the above functions will return -1.
1217 It should be noted that C<isl> does not guarantee that
1218 the basic sets or maps passed to C<fn> are disjoint.
1219 If this is required, then the user should call one of
1220 the following functions first.
1222 __isl_give isl_set *isl_set_make_disjoint(
1223 __isl_take isl_set *set);
1224 __isl_give isl_map *isl_map_make_disjoint(
1225 __isl_take isl_map *map);
1227 The number of basic sets in a set can be obtained
1230 int isl_set_n_basic_set(__isl_keep isl_set *set);
1232 To iterate over the constraints of a basic set or map, use
1234 #include <isl/constraint.h>
1236 int isl_basic_map_foreach_constraint(
1237 __isl_keep isl_basic_map *bmap,
1238 int (*fn)(__isl_take isl_constraint *c, void *user),
1240 void isl_constraint_free(struct isl_constraint *c);
1242 Again, the callback function C<fn> should return 0 if successful and
1243 -1 if an error occurs. In the latter case, or if any other error
1244 occurs, the above functions will return -1.
1245 The constraint C<c> represents either an equality or an inequality.
1246 Use the following function to find out whether a constraint
1247 represents an equality. If not, it represents an inequality.
1249 int isl_constraint_is_equality(
1250 __isl_keep isl_constraint *constraint);
1252 The coefficients of the constraints can be inspected using
1253 the following functions.
1255 void isl_constraint_get_constant(
1256 __isl_keep isl_constraint *constraint, isl_int *v);
1257 void isl_constraint_get_coefficient(
1258 __isl_keep isl_constraint *constraint,
1259 enum isl_dim_type type, int pos, isl_int *v);
1260 int isl_constraint_involves_dims(
1261 __isl_keep isl_constraint *constraint,
1262 enum isl_dim_type type, unsigned first, unsigned n);
1264 The explicit representations of the existentially quantified
1265 variables can be inspected using the following functions.
1266 Note that the user is only allowed to use these functions
1267 if the inspected set or map is the result of a call
1268 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1270 __isl_give isl_div *isl_constraint_div(
1271 __isl_keep isl_constraint *constraint, int pos);
1272 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1273 void isl_div_get_constant(__isl_keep isl_div *div,
1275 void isl_div_get_denominator(__isl_keep isl_div *div,
1277 void isl_div_get_coefficient(__isl_keep isl_div *div,
1278 enum isl_dim_type type, int pos, isl_int *v);
1280 To obtain the constraints of a basic set or map in matrix
1281 form, use the following functions.
1283 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1284 __isl_keep isl_basic_set *bset,
1285 enum isl_dim_type c1, enum isl_dim_type c2,
1286 enum isl_dim_type c3, enum isl_dim_type c4);
1287 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1288 __isl_keep isl_basic_set *bset,
1289 enum isl_dim_type c1, enum isl_dim_type c2,
1290 enum isl_dim_type c3, enum isl_dim_type c4);
1291 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1292 __isl_keep isl_basic_map *bmap,
1293 enum isl_dim_type c1,
1294 enum isl_dim_type c2, enum isl_dim_type c3,
1295 enum isl_dim_type c4, enum isl_dim_type c5);
1296 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1297 __isl_keep isl_basic_map *bmap,
1298 enum isl_dim_type c1,
1299 enum isl_dim_type c2, enum isl_dim_type c3,
1300 enum isl_dim_type c4, enum isl_dim_type c5);
1302 The C<isl_dim_type> arguments dictate the order in which
1303 different kinds of variables appear in the resulting matrix
1304 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1305 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1307 To check whether the description of a set or relation depends
1308 on one or more given dimensions, it is not necessary to iterate over all
1309 constraints. Instead the following functions can be used.
1311 int isl_basic_set_involves_dims(
1312 __isl_keep isl_basic_set *bset,
1313 enum isl_dim_type type, unsigned first, unsigned n);
1314 int isl_set_involves_dims(__isl_keep isl_set *set,
1315 enum isl_dim_type type, unsigned first, unsigned n);
1316 int isl_basic_map_involves_dims(
1317 __isl_keep isl_basic_map *bmap,
1318 enum isl_dim_type type, unsigned first, unsigned n);
1319 int isl_map_involves_dims(__isl_keep isl_map *map,
1320 enum isl_dim_type type, unsigned first, unsigned n);
1322 Similarly, the following functions can be used to check whether
1323 a given dimension is involved in any lower or upper bound.
1325 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1326 enum isl_dim_type type, unsigned pos);
1327 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1328 enum isl_dim_type type, unsigned pos);
1330 The identifiers or names of the domain and range spaces of a set
1331 or relation can be read off or set using the following functions.
1333 __isl_give isl_set *isl_set_set_tuple_id(
1334 __isl_take isl_set *set, __isl_take isl_id *id);
1335 __isl_give isl_id *isl_set_get_tuple_id(
1336 __isl_keep isl_set *set);
1337 __isl_give isl_map *isl_map_set_tuple_id(
1338 __isl_take isl_map *map, enum isl_dim_type type,
1339 __isl_take isl_id *id);
1340 __isl_give isl_map *isl_map_reset_tuple_id(
1341 __isl_take isl_map *map, enum isl_dim_type type);
1342 __isl_give isl_id *isl_map_get_tuple_id(
1343 __isl_keep isl_map *map, enum isl_dim_type type);
1345 const char *isl_basic_set_get_tuple_name(
1346 __isl_keep isl_basic_set *bset);
1347 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1348 __isl_take isl_basic_set *set, const char *s);
1349 const char *isl_set_get_tuple_name(
1350 __isl_keep isl_set *set);
1351 const char *isl_basic_map_get_tuple_name(
1352 __isl_keep isl_basic_map *bmap,
1353 enum isl_dim_type type);
1354 const char *isl_map_get_tuple_name(
1355 __isl_keep isl_map *map,
1356 enum isl_dim_type type);
1358 As with C<isl_dim_get_tuple_name>, the value returned points to
1359 an internal data structure.
1360 The identifiers, positions or names of individual dimensions can be
1361 read off using the following functions.
1363 __isl_give isl_set *isl_set_set_dim_id(
1364 __isl_take isl_set *set, enum isl_dim_type type,
1365 unsigned pos, __isl_take isl_id *id);
1366 __isl_give isl_id *isl_set_get_dim_id(
1367 __isl_keep isl_set *set, enum isl_dim_type type,
1369 __isl_give isl_map *isl_map_set_dim_id(
1370 __isl_take isl_map *map, enum isl_dim_type type,
1371 unsigned pos, __isl_take isl_id *id);
1372 __isl_give isl_id *isl_map_get_dim_id(
1373 __isl_keep isl_map *map, enum isl_dim_type type,
1376 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1377 enum isl_dim_type type, __isl_keep isl_id *id);
1378 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1379 enum isl_dim_type type, __isl_keep isl_id *id);
1381 const char *isl_constraint_get_dim_name(
1382 __isl_keep isl_constraint *constraint,
1383 enum isl_dim_type type, unsigned pos);
1384 const char *isl_basic_set_get_dim_name(
1385 __isl_keep isl_basic_set *bset,
1386 enum isl_dim_type type, unsigned pos);
1387 const char *isl_set_get_dim_name(
1388 __isl_keep isl_set *set,
1389 enum isl_dim_type type, unsigned pos);
1390 const char *isl_basic_map_get_dim_name(
1391 __isl_keep isl_basic_map *bmap,
1392 enum isl_dim_type type, unsigned pos);
1393 const char *isl_map_get_dim_name(
1394 __isl_keep isl_map *map,
1395 enum isl_dim_type type, unsigned pos);
1397 These functions are mostly useful to obtain the identifiers, positions
1398 or names of the parameters.
1402 =head3 Unary Properties
1408 The following functions test whether the given set or relation
1409 contains any integer points. The ``plain'' variants do not perform
1410 any computations, but simply check if the given set or relation
1411 is already known to be empty.
1413 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1414 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1415 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1416 int isl_set_is_empty(__isl_keep isl_set *set);
1417 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1418 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1419 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1420 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1421 int isl_map_is_empty(__isl_keep isl_map *map);
1422 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1424 =item * Universality
1426 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1427 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1428 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1430 =item * Single-valuedness
1432 int isl_map_is_single_valued(__isl_keep isl_map *map);
1433 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1437 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1438 int isl_map_is_injective(__isl_keep isl_map *map);
1439 int isl_union_map_plain_is_injective(
1440 __isl_keep isl_union_map *umap);
1441 int isl_union_map_is_injective(
1442 __isl_keep isl_union_map *umap);
1446 int isl_map_is_bijective(__isl_keep isl_map *map);
1447 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1451 The following functions check whether the domain of the given
1452 (basic) set is a wrapped relation.
1454 int isl_basic_set_is_wrapping(
1455 __isl_keep isl_basic_set *bset);
1456 int isl_set_is_wrapping(__isl_keep isl_set *set);
1458 =item * Internal Product
1460 int isl_basic_map_can_zip(
1461 __isl_keep isl_basic_map *bmap);
1462 int isl_map_can_zip(__isl_keep isl_map *map);
1464 Check whether the product of domain and range of the given relation
1466 i.e., whether both domain and range are nested relations.
1470 =head3 Binary Properties
1476 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1477 __isl_keep isl_set *set2);
1478 int isl_set_is_equal(__isl_keep isl_set *set1,
1479 __isl_keep isl_set *set2);
1480 int isl_union_set_is_equal(
1481 __isl_keep isl_union_set *uset1,
1482 __isl_keep isl_union_set *uset2);
1483 int isl_basic_map_is_equal(
1484 __isl_keep isl_basic_map *bmap1,
1485 __isl_keep isl_basic_map *bmap2);
1486 int isl_map_is_equal(__isl_keep isl_map *map1,
1487 __isl_keep isl_map *map2);
1488 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1489 __isl_keep isl_map *map2);
1490 int isl_union_map_is_equal(
1491 __isl_keep isl_union_map *umap1,
1492 __isl_keep isl_union_map *umap2);
1494 =item * Disjointness
1496 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1497 __isl_keep isl_set *set2);
1501 int isl_set_is_subset(__isl_keep isl_set *set1,
1502 __isl_keep isl_set *set2);
1503 int isl_set_is_strict_subset(
1504 __isl_keep isl_set *set1,
1505 __isl_keep isl_set *set2);
1506 int isl_union_set_is_subset(
1507 __isl_keep isl_union_set *uset1,
1508 __isl_keep isl_union_set *uset2);
1509 int isl_union_set_is_strict_subset(
1510 __isl_keep isl_union_set *uset1,
1511 __isl_keep isl_union_set *uset2);
1512 int isl_basic_map_is_subset(
1513 __isl_keep isl_basic_map *bmap1,
1514 __isl_keep isl_basic_map *bmap2);
1515 int isl_basic_map_is_strict_subset(
1516 __isl_keep isl_basic_map *bmap1,
1517 __isl_keep isl_basic_map *bmap2);
1518 int isl_map_is_subset(
1519 __isl_keep isl_map *map1,
1520 __isl_keep isl_map *map2);
1521 int isl_map_is_strict_subset(
1522 __isl_keep isl_map *map1,
1523 __isl_keep isl_map *map2);
1524 int isl_union_map_is_subset(
1525 __isl_keep isl_union_map *umap1,
1526 __isl_keep isl_union_map *umap2);
1527 int isl_union_map_is_strict_subset(
1528 __isl_keep isl_union_map *umap1,
1529 __isl_keep isl_union_map *umap2);
1533 =head2 Unary Operations
1539 __isl_give isl_set *isl_set_complement(
1540 __isl_take isl_set *set);
1544 __isl_give isl_basic_map *isl_basic_map_reverse(
1545 __isl_take isl_basic_map *bmap);
1546 __isl_give isl_map *isl_map_reverse(
1547 __isl_take isl_map *map);
1548 __isl_give isl_union_map *isl_union_map_reverse(
1549 __isl_take isl_union_map *umap);
1553 __isl_give isl_basic_set *isl_basic_set_project_out(
1554 __isl_take isl_basic_set *bset,
1555 enum isl_dim_type type, unsigned first, unsigned n);
1556 __isl_give isl_basic_map *isl_basic_map_project_out(
1557 __isl_take isl_basic_map *bmap,
1558 enum isl_dim_type type, unsigned first, unsigned n);
1559 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1560 enum isl_dim_type type, unsigned first, unsigned n);
1561 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1562 enum isl_dim_type type, unsigned first, unsigned n);
1563 __isl_give isl_basic_set *isl_basic_map_domain(
1564 __isl_take isl_basic_map *bmap);
1565 __isl_give isl_basic_set *isl_basic_map_range(
1566 __isl_take isl_basic_map *bmap);
1567 __isl_give isl_set *isl_map_domain(
1568 __isl_take isl_map *bmap);
1569 __isl_give isl_set *isl_map_range(
1570 __isl_take isl_map *map);
1571 __isl_give isl_union_set *isl_union_map_domain(
1572 __isl_take isl_union_map *umap);
1573 __isl_give isl_union_set *isl_union_map_range(
1574 __isl_take isl_union_map *umap);
1576 __isl_give isl_basic_map *isl_basic_map_domain_map(
1577 __isl_take isl_basic_map *bmap);
1578 __isl_give isl_basic_map *isl_basic_map_range_map(
1579 __isl_take isl_basic_map *bmap);
1580 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1581 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1582 __isl_give isl_union_map *isl_union_map_domain_map(
1583 __isl_take isl_union_map *umap);
1584 __isl_give isl_union_map *isl_union_map_range_map(
1585 __isl_take isl_union_map *umap);
1587 The functions above construct a (basic, regular or union) relation
1588 that maps (a wrapped version of) the input relation to its domain or range.
1592 __isl_give isl_set *isl_set_eliminate(
1593 __isl_take isl_set *set, enum isl_dim_type type,
1594 unsigned first, unsigned n);
1596 Eliminate the coefficients for the given dimensions from the constraints,
1597 without removing the dimensions.
1601 __isl_give isl_basic_set *isl_basic_set_fix(
1602 __isl_take isl_basic_set *bset,
1603 enum isl_dim_type type, unsigned pos,
1605 __isl_give isl_basic_set *isl_basic_set_fix_si(
1606 __isl_take isl_basic_set *bset,
1607 enum isl_dim_type type, unsigned pos, int value);
1608 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1609 enum isl_dim_type type, unsigned pos,
1611 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1612 enum isl_dim_type type, unsigned pos, int value);
1613 __isl_give isl_basic_map *isl_basic_map_fix_si(
1614 __isl_take isl_basic_map *bmap,
1615 enum isl_dim_type type, unsigned pos, int value);
1616 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1617 enum isl_dim_type type, unsigned pos, int value);
1619 Intersect the set or relation with the hyperplane where the given
1620 dimension has the fixed given value.
1622 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1623 enum isl_dim_type type1, int pos1,
1624 enum isl_dim_type type2, int pos2);
1625 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1626 enum isl_dim_type type1, int pos1,
1627 enum isl_dim_type type2, int pos2);
1629 Intersect the set or relation with the hyperplane where the given
1630 dimensions are equal to each other.
1632 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1633 enum isl_dim_type type1, int pos1,
1634 enum isl_dim_type type2, int pos2);
1636 Intersect the relation with the hyperplane where the given
1637 dimensions have opposite values.
1641 __isl_give isl_map *isl_set_identity(
1642 __isl_take isl_set *set);
1643 __isl_give isl_union_map *isl_union_set_identity(
1644 __isl_take isl_union_set *uset);
1646 Construct an identity relation on the given (union) set.
1650 __isl_give isl_basic_set *isl_basic_map_deltas(
1651 __isl_take isl_basic_map *bmap);
1652 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1653 __isl_give isl_union_set *isl_union_map_deltas(
1654 __isl_take isl_union_map *umap);
1656 These functions return a (basic) set containing the differences
1657 between image elements and corresponding domain elements in the input.
1659 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1660 __isl_take isl_basic_map *bmap);
1661 __isl_give isl_map *isl_map_deltas_map(
1662 __isl_take isl_map *map);
1663 __isl_give isl_union_map *isl_union_map_deltas_map(
1664 __isl_take isl_union_map *umap);
1666 The functions above construct a (basic, regular or union) relation
1667 that maps (a wrapped version of) the input relation to its delta set.
1671 Simplify the representation of a set or relation by trying
1672 to combine pairs of basic sets or relations into a single
1673 basic set or relation.
1675 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1676 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1677 __isl_give isl_union_set *isl_union_set_coalesce(
1678 __isl_take isl_union_set *uset);
1679 __isl_give isl_union_map *isl_union_map_coalesce(
1680 __isl_take isl_union_map *umap);
1682 =item * Detecting equalities
1684 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1685 __isl_take isl_basic_set *bset);
1686 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1687 __isl_take isl_basic_map *bmap);
1688 __isl_give isl_set *isl_set_detect_equalities(
1689 __isl_take isl_set *set);
1690 __isl_give isl_map *isl_map_detect_equalities(
1691 __isl_take isl_map *map);
1692 __isl_give isl_union_set *isl_union_set_detect_equalities(
1693 __isl_take isl_union_set *uset);
1694 __isl_give isl_union_map *isl_union_map_detect_equalities(
1695 __isl_take isl_union_map *umap);
1697 Simplify the representation of a set or relation by detecting implicit
1700 =item * Removing redundant constraints
1702 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1703 __isl_take isl_basic_set *bset);
1704 __isl_give isl_set *isl_set_remove_redundancies(
1705 __isl_take isl_set *set);
1706 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1707 __isl_take isl_basic_map *bmap);
1708 __isl_give isl_map *isl_map_remove_redundancies(
1709 __isl_take isl_map *map);
1713 __isl_give isl_basic_set *isl_set_convex_hull(
1714 __isl_take isl_set *set);
1715 __isl_give isl_basic_map *isl_map_convex_hull(
1716 __isl_take isl_map *map);
1718 If the input set or relation has any existentially quantified
1719 variables, then the result of these operations is currently undefined.
1723 __isl_give isl_basic_set *isl_set_simple_hull(
1724 __isl_take isl_set *set);
1725 __isl_give isl_basic_map *isl_map_simple_hull(
1726 __isl_take isl_map *map);
1727 __isl_give isl_union_map *isl_union_map_simple_hull(
1728 __isl_take isl_union_map *umap);
1730 These functions compute a single basic set or relation
1731 that contains the whole input set or relation.
1732 In particular, the output is described by translates
1733 of the constraints describing the basic sets or relations in the input.
1737 (See \autoref{s:simple hull}.)
1743 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1744 __isl_take isl_basic_set *bset);
1745 __isl_give isl_basic_set *isl_set_affine_hull(
1746 __isl_take isl_set *set);
1747 __isl_give isl_union_set *isl_union_set_affine_hull(
1748 __isl_take isl_union_set *uset);
1749 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1750 __isl_take isl_basic_map *bmap);
1751 __isl_give isl_basic_map *isl_map_affine_hull(
1752 __isl_take isl_map *map);
1753 __isl_give isl_union_map *isl_union_map_affine_hull(
1754 __isl_take isl_union_map *umap);
1756 In case of union sets and relations, the affine hull is computed
1759 =item * Polyhedral hull
1761 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1762 __isl_take isl_set *set);
1763 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1764 __isl_take isl_map *map);
1765 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1766 __isl_take isl_union_set *uset);
1767 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1768 __isl_take isl_union_map *umap);
1770 These functions compute a single basic set or relation
1771 not involving any existentially quantified variables
1772 that contains the whole input set or relation.
1773 In case of union sets and relations, the polyhedral hull is computed
1776 =item * Optimization
1778 #include <isl/ilp.h>
1779 enum isl_lp_result isl_basic_set_max(
1780 __isl_keep isl_basic_set *bset,
1781 __isl_keep isl_aff *obj, isl_int *opt)
1782 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1783 __isl_keep isl_aff *obj, isl_int *opt);
1784 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1785 __isl_keep isl_aff *obj, isl_int *opt);
1787 Compute the minimum or maximum of the integer affine expression C<obj>
1788 over the points in C<set>, returning the result in C<opt>.
1789 The return value may be one of C<isl_lp_error>,
1790 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1792 =item * Parametric optimization
1794 __isl_give isl_pw_aff *isl_set_dim_max(
1795 __isl_take isl_set *set, int pos);
1797 Compute the maximum of the given set dimension as a function of the
1798 parameters, but independently of the other set dimensions.
1799 For lexicographic optimization, see L<"Lexicographic Optimization">.
1803 The following functions compute either the set of (rational) coefficient
1804 values of valid constraints for the given set or the set of (rational)
1805 values satisfying the constraints with coefficients from the given set.
1806 Internally, these two sets of functions perform essentially the
1807 same operations, except that the set of coefficients is assumed to
1808 be a cone, while the set of values may be any polyhedron.
1809 The current implementation is based on the Farkas lemma and
1810 Fourier-Motzkin elimination, but this may change or be made optional
1811 in future. In particular, future implementations may use different
1812 dualization algorithms or skip the elimination step.
1814 __isl_give isl_basic_set *isl_basic_set_coefficients(
1815 __isl_take isl_basic_set *bset);
1816 __isl_give isl_basic_set *isl_set_coefficients(
1817 __isl_take isl_set *set);
1818 __isl_give isl_union_set *isl_union_set_coefficients(
1819 __isl_take isl_union_set *bset);
1820 __isl_give isl_basic_set *isl_basic_set_solutions(
1821 __isl_take isl_basic_set *bset);
1822 __isl_give isl_basic_set *isl_set_solutions(
1823 __isl_take isl_set *set);
1824 __isl_give isl_union_set *isl_union_set_solutions(
1825 __isl_take isl_union_set *bset);
1829 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1831 __isl_give isl_union_map *isl_union_map_power(
1832 __isl_take isl_union_map *umap, int *exact);
1834 Compute a parametric representation for all positive powers I<k> of C<map>.
1835 The result maps I<k> to a nested relation corresponding to the
1836 I<k>th power of C<map>.
1837 The result may be an overapproximation. If the result is known to be exact,
1838 then C<*exact> is set to C<1>.
1840 =item * Transitive closure
1842 __isl_give isl_map *isl_map_transitive_closure(
1843 __isl_take isl_map *map, int *exact);
1844 __isl_give isl_union_map *isl_union_map_transitive_closure(
1845 __isl_take isl_union_map *umap, int *exact);
1847 Compute the transitive closure of C<map>.
1848 The result may be an overapproximation. If the result is known to be exact,
1849 then C<*exact> is set to C<1>.
1851 =item * Reaching path lengths
1853 __isl_give isl_map *isl_map_reaching_path_lengths(
1854 __isl_take isl_map *map, int *exact);
1856 Compute a relation that maps each element in the range of C<map>
1857 to the lengths of all paths composed of edges in C<map> that
1858 end up in the given element.
1859 The result may be an overapproximation. If the result is known to be exact,
1860 then C<*exact> is set to C<1>.
1861 To compute the I<maximal> path length, the resulting relation
1862 should be postprocessed by C<isl_map_lexmax>.
1863 In particular, if the input relation is a dependence relation
1864 (mapping sources to sinks), then the maximal path length corresponds
1865 to the free schedule.
1866 Note, however, that C<isl_map_lexmax> expects the maximum to be
1867 finite, so if the path lengths are unbounded (possibly due to
1868 the overapproximation), then you will get an error message.
1872 __isl_give isl_basic_set *isl_basic_map_wrap(
1873 __isl_take isl_basic_map *bmap);
1874 __isl_give isl_set *isl_map_wrap(
1875 __isl_take isl_map *map);
1876 __isl_give isl_union_set *isl_union_map_wrap(
1877 __isl_take isl_union_map *umap);
1878 __isl_give isl_basic_map *isl_basic_set_unwrap(
1879 __isl_take isl_basic_set *bset);
1880 __isl_give isl_map *isl_set_unwrap(
1881 __isl_take isl_set *set);
1882 __isl_give isl_union_map *isl_union_set_unwrap(
1883 __isl_take isl_union_set *uset);
1887 Remove any internal structure of domain (and range) of the given
1888 set or relation. If there is any such internal structure in the input,
1889 then the name of the space is also removed.
1891 __isl_give isl_basic_set *isl_basic_set_flatten(
1892 __isl_take isl_basic_set *bset);
1893 __isl_give isl_set *isl_set_flatten(
1894 __isl_take isl_set *set);
1895 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1896 __isl_take isl_basic_map *bmap);
1897 __isl_give isl_map *isl_map_flatten_range(
1898 __isl_take isl_map *map);
1899 __isl_give isl_basic_map *isl_basic_map_flatten(
1900 __isl_take isl_basic_map *bmap);
1901 __isl_give isl_map *isl_map_flatten(
1902 __isl_take isl_map *map);
1904 __isl_give isl_map *isl_set_flatten_map(
1905 __isl_take isl_set *set);
1907 The function above constructs a relation
1908 that maps the input set to a flattened version of the set.
1912 Lift the input set to a space with extra dimensions corresponding
1913 to the existentially quantified variables in the input.
1914 In particular, the result lives in a wrapped map where the domain
1915 is the original space and the range corresponds to the original
1916 existentially quantified variables.
1918 __isl_give isl_basic_set *isl_basic_set_lift(
1919 __isl_take isl_basic_set *bset);
1920 __isl_give isl_set *isl_set_lift(
1921 __isl_take isl_set *set);
1922 __isl_give isl_union_set *isl_union_set_lift(
1923 __isl_take isl_union_set *uset);
1925 =item * Internal Product
1927 __isl_give isl_basic_map *isl_basic_map_zip(
1928 __isl_take isl_basic_map *bmap);
1929 __isl_give isl_map *isl_map_zip(
1930 __isl_take isl_map *map);
1931 __isl_give isl_union_map *isl_union_map_zip(
1932 __isl_take isl_union_map *umap);
1934 Given a relation with nested relations for domain and range,
1935 interchange the range of the domain with the domain of the range.
1937 =item * Aligning parameters
1939 __isl_give isl_set *isl_set_align_params(
1940 __isl_take isl_set *set,
1941 __isl_take isl_dim *model);
1942 __isl_give isl_map *isl_map_align_params(
1943 __isl_take isl_map *map,
1944 __isl_take isl_dim *model);
1946 Change the order of the parameters of the given set or relation
1947 such that the first parameters match those of C<model>.
1948 This may involve the introduction of extra parameters.
1949 All parameters need to be named.
1951 =item * Dimension manipulation
1953 __isl_give isl_set *isl_set_add_dims(
1954 __isl_take isl_set *set,
1955 enum isl_dim_type type, unsigned n);
1956 __isl_give isl_map *isl_map_add_dims(
1957 __isl_take isl_map *map,
1958 enum isl_dim_type type, unsigned n);
1960 It is usually not advisable to directly change the (input or output)
1961 space of a set or a relation as this removes the name and the internal
1962 structure of the space. However, the above functions can be useful
1963 to add new parameters, assuming
1964 C<isl_set_align_params> and C<isl_map_align_params>
1969 =head2 Binary Operations
1971 The two arguments of a binary operation not only need to live
1972 in the same C<isl_ctx>, they currently also need to have
1973 the same (number of) parameters.
1975 =head3 Basic Operations
1979 =item * Intersection
1981 __isl_give isl_basic_set *isl_basic_set_intersect(
1982 __isl_take isl_basic_set *bset1,
1983 __isl_take isl_basic_set *bset2);
1984 __isl_give isl_set *isl_set_intersect_params(
1985 __isl_take isl_set *set,
1986 __isl_take isl_set *params);
1987 __isl_give isl_set *isl_set_intersect(
1988 __isl_take isl_set *set1,
1989 __isl_take isl_set *set2);
1990 __isl_give isl_union_set *isl_union_set_intersect(
1991 __isl_take isl_union_set *uset1,
1992 __isl_take isl_union_set *uset2);
1993 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1994 __isl_take isl_basic_map *bmap,
1995 __isl_take isl_basic_set *bset);
1996 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1997 __isl_take isl_basic_map *bmap,
1998 __isl_take isl_basic_set *bset);
1999 __isl_give isl_basic_map *isl_basic_map_intersect(
2000 __isl_take isl_basic_map *bmap1,
2001 __isl_take isl_basic_map *bmap2);
2002 __isl_give isl_map *isl_map_intersect_params(
2003 __isl_take isl_map *map,
2004 __isl_take isl_set *params);
2005 __isl_give isl_map *isl_map_intersect_domain(
2006 __isl_take isl_map *map,
2007 __isl_take isl_set *set);
2008 __isl_give isl_map *isl_map_intersect_range(
2009 __isl_take isl_map *map,
2010 __isl_take isl_set *set);
2011 __isl_give isl_map *isl_map_intersect(
2012 __isl_take isl_map *map1,
2013 __isl_take isl_map *map2);
2014 __isl_give isl_union_map *isl_union_map_intersect_domain(
2015 __isl_take isl_union_map *umap,
2016 __isl_take isl_union_set *uset);
2017 __isl_give isl_union_map *isl_union_map_intersect_range(
2018 __isl_take isl_union_map *umap,
2019 __isl_take isl_union_set *uset);
2020 __isl_give isl_union_map *isl_union_map_intersect(
2021 __isl_take isl_union_map *umap1,
2022 __isl_take isl_union_map *umap2);
2026 __isl_give isl_set *isl_basic_set_union(
2027 __isl_take isl_basic_set *bset1,
2028 __isl_take isl_basic_set *bset2);
2029 __isl_give isl_map *isl_basic_map_union(
2030 __isl_take isl_basic_map *bmap1,
2031 __isl_take isl_basic_map *bmap2);
2032 __isl_give isl_set *isl_set_union(
2033 __isl_take isl_set *set1,
2034 __isl_take isl_set *set2);
2035 __isl_give isl_map *isl_map_union(
2036 __isl_take isl_map *map1,
2037 __isl_take isl_map *map2);
2038 __isl_give isl_union_set *isl_union_set_union(
2039 __isl_take isl_union_set *uset1,
2040 __isl_take isl_union_set *uset2);
2041 __isl_give isl_union_map *isl_union_map_union(
2042 __isl_take isl_union_map *umap1,
2043 __isl_take isl_union_map *umap2);
2045 =item * Set difference
2047 __isl_give isl_set *isl_set_subtract(
2048 __isl_take isl_set *set1,
2049 __isl_take isl_set *set2);
2050 __isl_give isl_map *isl_map_subtract(
2051 __isl_take isl_map *map1,
2052 __isl_take isl_map *map2);
2053 __isl_give isl_union_set *isl_union_set_subtract(
2054 __isl_take isl_union_set *uset1,
2055 __isl_take isl_union_set *uset2);
2056 __isl_give isl_union_map *isl_union_map_subtract(
2057 __isl_take isl_union_map *umap1,
2058 __isl_take isl_union_map *umap2);
2062 __isl_give isl_basic_set *isl_basic_set_apply(
2063 __isl_take isl_basic_set *bset,
2064 __isl_take isl_basic_map *bmap);
2065 __isl_give isl_set *isl_set_apply(
2066 __isl_take isl_set *set,
2067 __isl_take isl_map *map);
2068 __isl_give isl_union_set *isl_union_set_apply(
2069 __isl_take isl_union_set *uset,
2070 __isl_take isl_union_map *umap);
2071 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2072 __isl_take isl_basic_map *bmap1,
2073 __isl_take isl_basic_map *bmap2);
2074 __isl_give isl_basic_map *isl_basic_map_apply_range(
2075 __isl_take isl_basic_map *bmap1,
2076 __isl_take isl_basic_map *bmap2);
2077 __isl_give isl_map *isl_map_apply_domain(
2078 __isl_take isl_map *map1,
2079 __isl_take isl_map *map2);
2080 __isl_give isl_union_map *isl_union_map_apply_domain(
2081 __isl_take isl_union_map *umap1,
2082 __isl_take isl_union_map *umap2);
2083 __isl_give isl_map *isl_map_apply_range(
2084 __isl_take isl_map *map1,
2085 __isl_take isl_map *map2);
2086 __isl_give isl_union_map *isl_union_map_apply_range(
2087 __isl_take isl_union_map *umap1,
2088 __isl_take isl_union_map *umap2);
2090 =item * Cartesian Product
2092 __isl_give isl_set *isl_set_product(
2093 __isl_take isl_set *set1,
2094 __isl_take isl_set *set2);
2095 __isl_give isl_union_set *isl_union_set_product(
2096 __isl_take isl_union_set *uset1,
2097 __isl_take isl_union_set *uset2);
2098 __isl_give isl_basic_map *isl_basic_map_range_product(
2099 __isl_take isl_basic_map *bmap1,
2100 __isl_take isl_basic_map *bmap2);
2101 __isl_give isl_map *isl_map_range_product(
2102 __isl_take isl_map *map1,
2103 __isl_take isl_map *map2);
2104 __isl_give isl_union_map *isl_union_map_range_product(
2105 __isl_take isl_union_map *umap1,
2106 __isl_take isl_union_map *umap2);
2107 __isl_give isl_map *isl_map_product(
2108 __isl_take isl_map *map1,
2109 __isl_take isl_map *map2);
2110 __isl_give isl_union_map *isl_union_map_product(
2111 __isl_take isl_union_map *umap1,
2112 __isl_take isl_union_map *umap2);
2114 The above functions compute the cross product of the given
2115 sets or relations. The domains and ranges of the results
2116 are wrapped maps between domains and ranges of the inputs.
2117 To obtain a ``flat'' product, use the following functions
2120 __isl_give isl_basic_set *isl_basic_set_flat_product(
2121 __isl_take isl_basic_set *bset1,
2122 __isl_take isl_basic_set *bset2);
2123 __isl_give isl_set *isl_set_flat_product(
2124 __isl_take isl_set *set1,
2125 __isl_take isl_set *set2);
2126 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2127 __isl_take isl_basic_map *bmap1,
2128 __isl_take isl_basic_map *bmap2);
2129 __isl_give isl_map *isl_map_flat_range_product(
2130 __isl_take isl_map *map1,
2131 __isl_take isl_map *map2);
2132 __isl_give isl_union_map *isl_union_map_flat_range_product(
2133 __isl_take isl_union_map *umap1,
2134 __isl_take isl_union_map *umap2);
2135 __isl_give isl_basic_map *isl_basic_map_flat_product(
2136 __isl_take isl_basic_map *bmap1,
2137 __isl_take isl_basic_map *bmap2);
2138 __isl_give isl_map *isl_map_flat_product(
2139 __isl_take isl_map *map1,
2140 __isl_take isl_map *map2);
2142 =item * Simplification
2144 __isl_give isl_basic_set *isl_basic_set_gist(
2145 __isl_take isl_basic_set *bset,
2146 __isl_take isl_basic_set *context);
2147 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2148 __isl_take isl_set *context);
2149 __isl_give isl_union_set *isl_union_set_gist(
2150 __isl_take isl_union_set *uset,
2151 __isl_take isl_union_set *context);
2152 __isl_give isl_basic_map *isl_basic_map_gist(
2153 __isl_take isl_basic_map *bmap,
2154 __isl_take isl_basic_map *context);
2155 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2156 __isl_take isl_map *context);
2157 __isl_give isl_union_map *isl_union_map_gist(
2158 __isl_take isl_union_map *umap,
2159 __isl_take isl_union_map *context);
2161 The gist operation returns a set or relation that has the
2162 same intersection with the context as the input set or relation.
2163 Any implicit equality in the intersection is made explicit in the result,
2164 while all inequalities that are redundant with respect to the intersection
2166 In case of union sets and relations, the gist operation is performed
2171 =head3 Lexicographic Optimization
2173 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2174 the following functions
2175 compute a set that contains the lexicographic minimum or maximum
2176 of the elements in C<set> (or C<bset>) for those values of the parameters
2177 that satisfy C<dom>.
2178 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2179 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2181 In other words, the union of the parameter values
2182 for which the result is non-empty and of C<*empty>
2185 __isl_give isl_set *isl_basic_set_partial_lexmin(
2186 __isl_take isl_basic_set *bset,
2187 __isl_take isl_basic_set *dom,
2188 __isl_give isl_set **empty);
2189 __isl_give isl_set *isl_basic_set_partial_lexmax(
2190 __isl_take isl_basic_set *bset,
2191 __isl_take isl_basic_set *dom,
2192 __isl_give isl_set **empty);
2193 __isl_give isl_set *isl_set_partial_lexmin(
2194 __isl_take isl_set *set, __isl_take isl_set *dom,
2195 __isl_give isl_set **empty);
2196 __isl_give isl_set *isl_set_partial_lexmax(
2197 __isl_take isl_set *set, __isl_take isl_set *dom,
2198 __isl_give isl_set **empty);
2200 Given a (basic) set C<set> (or C<bset>), the following functions simply
2201 return a set containing the lexicographic minimum or maximum
2202 of the elements in C<set> (or C<bset>).
2203 In case of union sets, the optimum is computed per space.
2205 __isl_give isl_set *isl_basic_set_lexmin(
2206 __isl_take isl_basic_set *bset);
2207 __isl_give isl_set *isl_basic_set_lexmax(
2208 __isl_take isl_basic_set *bset);
2209 __isl_give isl_set *isl_set_lexmin(
2210 __isl_take isl_set *set);
2211 __isl_give isl_set *isl_set_lexmax(
2212 __isl_take isl_set *set);
2213 __isl_give isl_union_set *isl_union_set_lexmin(
2214 __isl_take isl_union_set *uset);
2215 __isl_give isl_union_set *isl_union_set_lexmax(
2216 __isl_take isl_union_set *uset);
2218 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2219 the following functions
2220 compute a relation that maps each element of C<dom>
2221 to the single lexicographic minimum or maximum
2222 of the elements that are associated to that same
2223 element in C<map> (or C<bmap>).
2224 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2225 that contains the elements in C<dom> that do not map
2226 to any elements in C<map> (or C<bmap>).
2227 In other words, the union of the domain of the result and of C<*empty>
2230 __isl_give isl_map *isl_basic_map_partial_lexmax(
2231 __isl_take isl_basic_map *bmap,
2232 __isl_take isl_basic_set *dom,
2233 __isl_give isl_set **empty);
2234 __isl_give isl_map *isl_basic_map_partial_lexmin(
2235 __isl_take isl_basic_map *bmap,
2236 __isl_take isl_basic_set *dom,
2237 __isl_give isl_set **empty);
2238 __isl_give isl_map *isl_map_partial_lexmax(
2239 __isl_take isl_map *map, __isl_take isl_set *dom,
2240 __isl_give isl_set **empty);
2241 __isl_give isl_map *isl_map_partial_lexmin(
2242 __isl_take isl_map *map, __isl_take isl_set *dom,
2243 __isl_give isl_set **empty);
2245 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2246 return a map mapping each element in the domain of
2247 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2248 of all elements associated to that element.
2249 In case of union relations, the optimum is computed per space.
2251 __isl_give isl_map *isl_basic_map_lexmin(
2252 __isl_take isl_basic_map *bmap);
2253 __isl_give isl_map *isl_basic_map_lexmax(
2254 __isl_take isl_basic_map *bmap);
2255 __isl_give isl_map *isl_map_lexmin(
2256 __isl_take isl_map *map);
2257 __isl_give isl_map *isl_map_lexmax(
2258 __isl_take isl_map *map);
2259 __isl_give isl_union_map *isl_union_map_lexmin(
2260 __isl_take isl_union_map *umap);
2261 __isl_give isl_union_map *isl_union_map_lexmax(
2262 __isl_take isl_union_map *umap);
2266 Lists are defined over several element types, including
2267 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2268 Here we take lists of C<isl_set>s as an example.
2269 Lists can be created, copied and freed using the following functions.
2271 #include <isl/list.h>
2272 __isl_give isl_set_list *isl_set_list_from_set(
2273 __isl_take struct isl_set *el);
2274 __isl_give isl_set_list *isl_set_list_alloc(
2275 isl_ctx *ctx, int n);
2276 __isl_give isl_set_list *isl_set_list_copy(
2277 __isl_keep isl_set_list *list);
2278 __isl_give isl_set_list *isl_set_list_add(
2279 __isl_take isl_set_list *list,
2280 __isl_take isl_set *el);
2281 __isl_give isl_set_list *isl_set_list_concat(
2282 __isl_take isl_set_list *list1,
2283 __isl_take isl_set_list *list2);
2284 void *isl_set_list_free(__isl_take isl_set_list *list);
2286 C<isl_set_list_alloc> creates an empty list with a capacity for
2287 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2290 Lists can be inspected using the following functions.
2292 #include <isl/list.h>
2293 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2294 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2295 __isl_give struct isl_set *isl_set_list_get_set(
2296 __isl_keep isl_set_list *list, int index);
2297 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2298 int (*fn)(__isl_take struct isl_set *el, void *user),
2301 Lists can be printed using
2303 #include <isl/list.h>
2304 __isl_give isl_printer *isl_printer_print_set_list(
2305 __isl_take isl_printer *p,
2306 __isl_keep isl_set_list *list);
2310 Matrices can be created, copied and freed using the following functions.
2312 #include <isl/mat.h>
2313 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2314 unsigned n_row, unsigned n_col);
2315 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2316 void isl_mat_free(__isl_take isl_mat *mat);
2318 Note that the elements of a newly created matrix may have arbitrary values.
2319 The elements can be changed and inspected using the following functions.
2321 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2322 int isl_mat_rows(__isl_keep isl_mat *mat);
2323 int isl_mat_cols(__isl_keep isl_mat *mat);
2324 int isl_mat_get_element(__isl_keep isl_mat *mat,
2325 int row, int col, isl_int *v);
2326 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2327 int row, int col, isl_int v);
2328 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2329 int row, int col, int v);
2331 C<isl_mat_get_element> will return a negative value if anything went wrong.
2332 In that case, the value of C<*v> is undefined.
2334 The following function can be used to compute the (right) inverse
2335 of a matrix, i.e., a matrix such that the product of the original
2336 and the inverse (in that order) is a multiple of the identity matrix.
2337 The input matrix is assumed to be of full row-rank.
2339 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2341 The following function can be used to compute the (right) kernel
2342 (or null space) of a matrix, i.e., a matrix such that the product of
2343 the original and the kernel (in that order) is the zero matrix.
2345 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2347 =head2 Piecewise Quasi Affine Expressions
2349 The zero quasi affine expression can be created using
2351 __isl_give isl_aff *isl_aff_zero(
2352 __isl_take isl_local_space *ls);
2354 A quasi affine expression can also be initialized from an C<isl_div>:
2356 #include <isl/div.h>
2357 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2359 An empty piecewise quasi affine expression (one with no cells)
2360 or a piecewise quasi affine expression with a single cell can
2361 be created using the following functions.
2363 #include <isl/aff.h>
2364 __isl_give isl_pw_aff *isl_pw_aff_empty(
2365 __isl_take isl_dim *dim);
2366 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2367 __isl_take isl_set *set, __isl_take isl_aff *aff);
2368 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2369 __isl_take isl_aff *aff);
2371 Quasi affine expressions can be copied and freed using
2373 #include <isl/aff.h>
2374 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2375 void *isl_aff_free(__isl_take isl_aff *aff);
2377 __isl_give isl_pw_aff *isl_pw_aff_copy(
2378 __isl_keep isl_pw_aff *pwaff);
2379 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2381 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2382 using the following function. The constraint is required to have
2383 a non-zero coefficient for the specified dimension.
2385 #include <isl/constraint.h>
2386 __isl_give isl_aff *isl_constraint_get_bound(
2387 __isl_keep isl_constraint *constraint,
2388 enum isl_dim_type type, int pos);
2390 The entire affine expression of the constraint can also be extracted
2391 using the following function.
2393 #include <isl/constraint.h>
2394 __isl_give isl_aff *isl_constraint_get_aff(
2395 __isl_keep isl_constraint *constraint);
2397 Conversely, an equality constraint equating
2398 the affine expression to zero or an inequality constraint enforcing
2399 the affine expression to be non-negative, can be constructed using
2401 __isl_give isl_constraint *isl_equality_from_aff(
2402 __isl_take isl_aff *aff);
2403 __isl_give isl_constraint *isl_inequality_from_aff(
2404 __isl_take isl_aff *aff);
2406 The expression can be inspected using
2408 #include <isl/aff.h>
2409 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2410 int isl_aff_dim(__isl_keep isl_aff *aff,
2411 enum isl_dim_type type);
2412 __isl_give isl_local_space *isl_aff_get_local_space(
2413 __isl_keep isl_aff *aff);
2414 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2415 enum isl_dim_type type, unsigned pos);
2416 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2418 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2419 enum isl_dim_type type, int pos, isl_int *v);
2420 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2422 __isl_give isl_div *isl_aff_get_div(
2423 __isl_keep isl_aff *aff, int pos);
2425 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2426 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2428 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2429 enum isl_dim_type type, unsigned first, unsigned n);
2430 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2431 enum isl_dim_type type, unsigned first, unsigned n);
2433 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2434 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2435 enum isl_dim_type type);
2436 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2438 It can be modified using
2440 #include <isl/aff.h>
2441 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2442 __isl_take isl_pw_aff *pwaff,
2443 __isl_take isl_id *id);
2444 __isl_give isl_aff *isl_aff_set_dim_name(
2445 __isl_take isl_aff *aff, enum isl_dim_type type,
2446 unsigned pos, const char *s);
2447 __isl_give isl_aff *isl_aff_set_constant(
2448 __isl_take isl_aff *aff, isl_int v);
2449 __isl_give isl_aff *isl_aff_set_constant_si(
2450 __isl_take isl_aff *aff, int v);
2451 __isl_give isl_aff *isl_aff_set_coefficient(
2452 __isl_take isl_aff *aff,
2453 enum isl_dim_type type, int pos, isl_int v);
2454 __isl_give isl_aff *isl_aff_set_coefficient_si(
2455 __isl_take isl_aff *aff,
2456 enum isl_dim_type type, int pos, int v);
2457 __isl_give isl_aff *isl_aff_set_denominator(
2458 __isl_take isl_aff *aff, isl_int v);
2460 __isl_give isl_aff *isl_aff_add_constant(
2461 __isl_take isl_aff *aff, isl_int v);
2462 __isl_give isl_aff *isl_aff_add_constant_si(
2463 __isl_take isl_aff *aff, int v);
2464 __isl_give isl_aff *isl_aff_add_coefficient(
2465 __isl_take isl_aff *aff,
2466 enum isl_dim_type type, int pos, isl_int v);
2467 __isl_give isl_aff *isl_aff_add_coefficient_si(
2468 __isl_take isl_aff *aff,
2469 enum isl_dim_type type, int pos, int v);
2471 __isl_give isl_aff *isl_aff_insert_dims(
2472 __isl_take isl_aff *aff,
2473 enum isl_dim_type type, unsigned first, unsigned n);
2474 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2475 __isl_take isl_pw_aff *pwaff,
2476 enum isl_dim_type type, unsigned first, unsigned n);
2477 __isl_give isl_aff *isl_aff_add_dims(
2478 __isl_take isl_aff *aff,
2479 enum isl_dim_type type, unsigned n);
2480 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2481 __isl_take isl_pw_aff *pwaff,
2482 enum isl_dim_type type, unsigned n);
2483 __isl_give isl_aff *isl_aff_drop_dims(
2484 __isl_take isl_aff *aff,
2485 enum isl_dim_type type, unsigned first, unsigned n);
2486 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2487 __isl_take isl_pw_aff *pwaff,
2488 enum isl_dim_type type, unsigned first, unsigned n);
2490 Note that the C<set_constant> and C<set_coefficient> functions
2491 set the I<numerator> of the constant or coefficient, while
2492 C<add_constant> and C<add_coefficient> add an integer value to
2493 the possibly rational constant or coefficient.
2495 To check whether an affine expressions is obviously zero
2496 or obviously equal to some other affine expression, use
2498 #include <isl/aff.h>
2499 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2500 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2501 __isl_keep isl_aff *aff2);
2505 #include <isl/aff.h>
2506 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2507 __isl_take isl_aff *aff2);
2508 __isl_give isl_pw_aff *isl_pw_aff_add(
2509 __isl_take isl_pw_aff *pwaff1,
2510 __isl_take isl_pw_aff *pwaff2);
2511 __isl_give isl_pw_aff *isl_pw_aff_min(
2512 __isl_take isl_pw_aff *pwaff1,
2513 __isl_take isl_pw_aff *pwaff2);
2514 __isl_give isl_pw_aff *isl_pw_aff_max(
2515 __isl_take isl_pw_aff *pwaff1,
2516 __isl_take isl_pw_aff *pwaff2);
2517 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2518 __isl_take isl_aff *aff2);
2519 __isl_give isl_pw_aff *isl_pw_aff_sub(
2520 __isl_take isl_pw_aff *pwaff1,
2521 __isl_take isl_pw_aff *pwaff2);
2522 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2523 __isl_give isl_pw_aff *isl_pw_aff_neg(
2524 __isl_take isl_pw_aff *pwaff);
2525 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2526 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2527 __isl_take isl_pw_aff *pwaff);
2528 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2529 __isl_give isl_pw_aff *isl_pw_aff_floor(
2530 __isl_take isl_pw_aff *pwaff);
2531 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2533 __isl_give isl_pw_aff *isl_pw_aff_scale(
2534 __isl_take isl_pw_aff *pwaff, isl_int f);
2535 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2537 __isl_give isl_aff *isl_aff_scale_down_ui(
2538 __isl_take isl_aff *aff, unsigned f);
2539 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2540 __isl_take isl_pw_aff *pwaff, isl_int f);
2542 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2543 __isl_take isl_pw_aff_list *list);
2544 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2545 __isl_take isl_pw_aff_list *list);
2547 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2548 __isl_take isl_pw_aff *pwqp);
2550 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2551 __isl_take isl_pw_aff *pwaff,
2552 __isl_take isl_dim *model);
2554 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2555 __isl_take isl_set *context);
2556 __isl_give isl_pw_aff *isl_pw_aff_gist(
2557 __isl_take isl_pw_aff *pwaff,
2558 __isl_take isl_set *context);
2560 __isl_give isl_set *isl_pw_aff_domain(
2561 __isl_take isl_pw_aff *pwaff);
2563 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2564 __isl_take isl_aff *aff2);
2565 __isl_give isl_pw_aff *isl_pw_aff_mul(
2566 __isl_take isl_pw_aff *pwaff1,
2567 __isl_take isl_pw_aff *pwaff2);
2569 When multiplying two affine expressions, at least one of the two needs
2572 #include <isl/aff.h>
2573 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2574 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2575 __isl_give isl_set *isl_pw_aff_eq_set(
2576 __isl_take isl_pw_aff *pwaff1,
2577 __isl_take isl_pw_aff *pwaff2);
2578 __isl_give isl_set *isl_pw_aff_ne_set(
2579 __isl_take isl_pw_aff *pwaff1,
2580 __isl_take isl_pw_aff *pwaff2);
2581 __isl_give isl_set *isl_pw_aff_le_set(
2582 __isl_take isl_pw_aff *pwaff1,
2583 __isl_take isl_pw_aff *pwaff2);
2584 __isl_give isl_set *isl_pw_aff_lt_set(
2585 __isl_take isl_pw_aff *pwaff1,
2586 __isl_take isl_pw_aff *pwaff2);
2587 __isl_give isl_set *isl_pw_aff_ge_set(
2588 __isl_take isl_pw_aff *pwaff1,
2589 __isl_take isl_pw_aff *pwaff2);
2590 __isl_give isl_set *isl_pw_aff_gt_set(
2591 __isl_take isl_pw_aff *pwaff1,
2592 __isl_take isl_pw_aff *pwaff2);
2594 __isl_give isl_set *isl_pw_aff_list_eq_set(
2595 __isl_take isl_pw_aff_list *list1,
2596 __isl_take isl_pw_aff_list *list2);
2597 __isl_give isl_set *isl_pw_aff_list_ne_set(
2598 __isl_take isl_pw_aff_list *list1,
2599 __isl_take isl_pw_aff_list *list2);
2600 __isl_give isl_set *isl_pw_aff_list_le_set(
2601 __isl_take isl_pw_aff_list *list1,
2602 __isl_take isl_pw_aff_list *list2);
2603 __isl_give isl_set *isl_pw_aff_list_lt_set(
2604 __isl_take isl_pw_aff_list *list1,
2605 __isl_take isl_pw_aff_list *list2);
2606 __isl_give isl_set *isl_pw_aff_list_ge_set(
2607 __isl_take isl_pw_aff_list *list1,
2608 __isl_take isl_pw_aff_list *list2);
2609 __isl_give isl_set *isl_pw_aff_list_gt_set(
2610 __isl_take isl_pw_aff_list *list1,
2611 __isl_take isl_pw_aff_list *list2);
2613 The function C<isl_aff_ge_basic_set> returns a basic set
2614 containing those elements in the shared space
2615 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2616 The function C<isl_aff_ge_set> returns a set
2617 containing those elements in the shared domain
2618 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2619 The functions operating on C<isl_pw_aff_list> apply the corresponding
2620 C<isl_pw_aff> function to each pair of elements in the two lists.
2622 #include <isl/aff.h>
2623 __isl_give isl_set *isl_pw_aff_nonneg_set(
2624 __isl_take isl_pw_aff *pwaff);
2625 __isl_give isl_set *isl_pw_aff_zero_set(
2626 __isl_take isl_pw_aff *pwaff);
2627 __isl_give isl_set *isl_pw_aff_non_zero_set(
2628 __isl_take isl_pw_aff *pwaff);
2630 The function C<isl_pw_aff_nonneg_set> returns a set
2631 containing those elements in the domain
2632 of C<pwaff> where C<pwaff> is non-negative.
2634 #include <isl/aff.h>
2635 __isl_give isl_pw_aff *isl_pw_aff_cond(
2636 __isl_take isl_set *cond,
2637 __isl_take isl_pw_aff *pwaff_true,
2638 __isl_take isl_pw_aff *pwaff_false);
2640 The function C<isl_pw_aff_cond> performs a conditional operator
2641 and returns an expression that is equal to C<pwaff_true>
2642 for elements in C<cond> and equal to C<pwaff_false> for elements
2645 #include <isl/aff.h>
2646 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2647 __isl_take isl_pw_aff *pwaff1,
2648 __isl_take isl_pw_aff *pwaff2);
2650 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2651 expression with a domain that is the union of those of C<pwaff1> and
2652 C<pwaff2> and such that on each cell, the quasi-affine expression is
2653 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2654 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2655 associated expression is the defined one.
2657 An expression can be printed using
2659 #include <isl/aff.h>
2660 __isl_give isl_printer *isl_printer_print_aff(
2661 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2663 __isl_give isl_printer *isl_printer_print_pw_aff(
2664 __isl_take isl_printer *p,
2665 __isl_keep isl_pw_aff *pwaff);
2669 Points are elements of a set. They can be used to construct
2670 simple sets (boxes) or they can be used to represent the
2671 individual elements of a set.
2672 The zero point (the origin) can be created using
2674 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2676 The coordinates of a point can be inspected, set and changed
2679 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2680 enum isl_dim_type type, int pos, isl_int *v);
2681 __isl_give isl_point *isl_point_set_coordinate(
2682 __isl_take isl_point *pnt,
2683 enum isl_dim_type type, int pos, isl_int v);
2685 __isl_give isl_point *isl_point_add_ui(
2686 __isl_take isl_point *pnt,
2687 enum isl_dim_type type, int pos, unsigned val);
2688 __isl_give isl_point *isl_point_sub_ui(
2689 __isl_take isl_point *pnt,
2690 enum isl_dim_type type, int pos, unsigned val);
2692 Other properties can be obtained using
2694 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2696 Points can be copied or freed using
2698 __isl_give isl_point *isl_point_copy(
2699 __isl_keep isl_point *pnt);
2700 void isl_point_free(__isl_take isl_point *pnt);
2702 A singleton set can be created from a point using
2704 __isl_give isl_basic_set *isl_basic_set_from_point(
2705 __isl_take isl_point *pnt);
2706 __isl_give isl_set *isl_set_from_point(
2707 __isl_take isl_point *pnt);
2709 and a box can be created from two opposite extremal points using
2711 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2712 __isl_take isl_point *pnt1,
2713 __isl_take isl_point *pnt2);
2714 __isl_give isl_set *isl_set_box_from_points(
2715 __isl_take isl_point *pnt1,
2716 __isl_take isl_point *pnt2);
2718 All elements of a B<bounded> (union) set can be enumerated using
2719 the following functions.
2721 int isl_set_foreach_point(__isl_keep isl_set *set,
2722 int (*fn)(__isl_take isl_point *pnt, void *user),
2724 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2725 int (*fn)(__isl_take isl_point *pnt, void *user),
2728 The function C<fn> is called for each integer point in
2729 C<set> with as second argument the last argument of
2730 the C<isl_set_foreach_point> call. The function C<fn>
2731 should return C<0> on success and C<-1> on failure.
2732 In the latter case, C<isl_set_foreach_point> will stop
2733 enumerating and return C<-1> as well.
2734 If the enumeration is performed successfully and to completion,
2735 then C<isl_set_foreach_point> returns C<0>.
2737 To obtain a single point of a (basic) set, use
2739 __isl_give isl_point *isl_basic_set_sample_point(
2740 __isl_take isl_basic_set *bset);
2741 __isl_give isl_point *isl_set_sample_point(
2742 __isl_take isl_set *set);
2744 If C<set> does not contain any (integer) points, then the
2745 resulting point will be ``void'', a property that can be
2748 int isl_point_is_void(__isl_keep isl_point *pnt);
2750 =head2 Piecewise Quasipolynomials
2752 A piecewise quasipolynomial is a particular kind of function that maps
2753 a parametric point to a rational value.
2754 More specifically, a quasipolynomial is a polynomial expression in greatest
2755 integer parts of affine expressions of parameters and variables.
2756 A piecewise quasipolynomial is a subdivision of a given parametric
2757 domain into disjoint cells with a quasipolynomial associated to
2758 each cell. The value of the piecewise quasipolynomial at a given
2759 point is the value of the quasipolynomial associated to the cell
2760 that contains the point. Outside of the union of cells,
2761 the value is assumed to be zero.
2762 For example, the piecewise quasipolynomial
2764 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2766 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2767 A given piecewise quasipolynomial has a fixed domain dimension.
2768 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2769 defined over different domains.
2770 Piecewise quasipolynomials are mainly used by the C<barvinok>
2771 library for representing the number of elements in a parametric set or map.
2772 For example, the piecewise quasipolynomial above represents
2773 the number of points in the map
2775 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2777 =head3 Printing (Piecewise) Quasipolynomials
2779 Quasipolynomials and piecewise quasipolynomials can be printed
2780 using the following functions.
2782 __isl_give isl_printer *isl_printer_print_qpolynomial(
2783 __isl_take isl_printer *p,
2784 __isl_keep isl_qpolynomial *qp);
2786 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2787 __isl_take isl_printer *p,
2788 __isl_keep isl_pw_qpolynomial *pwqp);
2790 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2791 __isl_take isl_printer *p,
2792 __isl_keep isl_union_pw_qpolynomial *upwqp);
2794 The output format of the printer
2795 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2796 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2798 In case of printing in C<ISL_FORMAT_C>, the user may want
2799 to set the names of all dimensions
2801 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2802 __isl_take isl_qpolynomial *qp,
2803 enum isl_dim_type type, unsigned pos,
2805 __isl_give isl_pw_qpolynomial *
2806 isl_pw_qpolynomial_set_dim_name(
2807 __isl_take isl_pw_qpolynomial *pwqp,
2808 enum isl_dim_type type, unsigned pos,
2811 =head3 Creating New (Piecewise) Quasipolynomials
2813 Some simple quasipolynomials can be created using the following functions.
2814 More complicated quasipolynomials can be created by applying
2815 operations such as addition and multiplication
2816 on the resulting quasipolynomials
2818 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2819 __isl_take isl_dim *dim);
2820 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2821 __isl_take isl_dim *dim);
2822 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2823 __isl_take isl_dim *dim);
2824 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2825 __isl_take isl_dim *dim);
2826 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2827 __isl_take isl_dim *dim);
2828 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2829 __isl_take isl_dim *dim,
2830 const isl_int n, const isl_int d);
2831 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2832 __isl_take isl_div *div);
2833 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2834 __isl_take isl_dim *dim,
2835 enum isl_dim_type type, unsigned pos);
2836 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2837 __isl_take isl_aff *aff);
2839 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2840 with a single cell can be created using the following functions.
2841 Multiple of these single cell piecewise quasipolynomials can
2842 be combined to create more complicated piecewise quasipolynomials.
2844 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2845 __isl_take isl_dim *dim);
2846 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2847 __isl_take isl_set *set,
2848 __isl_take isl_qpolynomial *qp);
2849 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2850 __isl_take isl_qpolynomial *qp);
2851 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2852 __isl_take isl_pw_aff *pwaff);
2854 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2855 __isl_take isl_dim *dim);
2856 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2857 __isl_take isl_pw_qpolynomial *pwqp);
2858 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2859 __isl_take isl_union_pw_qpolynomial *upwqp,
2860 __isl_take isl_pw_qpolynomial *pwqp);
2862 Quasipolynomials can be copied and freed again using the following
2865 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2866 __isl_keep isl_qpolynomial *qp);
2867 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2869 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2870 __isl_keep isl_pw_qpolynomial *pwqp);
2871 void *isl_pw_qpolynomial_free(
2872 __isl_take isl_pw_qpolynomial *pwqp);
2874 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2875 __isl_keep isl_union_pw_qpolynomial *upwqp);
2876 void isl_union_pw_qpolynomial_free(
2877 __isl_take isl_union_pw_qpolynomial *upwqp);
2879 =head3 Inspecting (Piecewise) Quasipolynomials
2881 To iterate over all piecewise quasipolynomials in a union
2882 piecewise quasipolynomial, use the following function
2884 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2885 __isl_keep isl_union_pw_qpolynomial *upwqp,
2886 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2889 To extract the piecewise quasipolynomial from a union with a given dimension
2892 __isl_give isl_pw_qpolynomial *
2893 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2894 __isl_keep isl_union_pw_qpolynomial *upwqp,
2895 __isl_take isl_dim *dim);
2897 To iterate over the cells in a piecewise quasipolynomial,
2898 use either of the following two functions
2900 int isl_pw_qpolynomial_foreach_piece(
2901 __isl_keep isl_pw_qpolynomial *pwqp,
2902 int (*fn)(__isl_take isl_set *set,
2903 __isl_take isl_qpolynomial *qp,
2904 void *user), void *user);
2905 int isl_pw_qpolynomial_foreach_lifted_piece(
2906 __isl_keep isl_pw_qpolynomial *pwqp,
2907 int (*fn)(__isl_take isl_set *set,
2908 __isl_take isl_qpolynomial *qp,
2909 void *user), void *user);
2911 As usual, the function C<fn> should return C<0> on success
2912 and C<-1> on failure. The difference between
2913 C<isl_pw_qpolynomial_foreach_piece> and
2914 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2915 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2916 compute unique representations for all existentially quantified
2917 variables and then turn these existentially quantified variables
2918 into extra set variables, adapting the associated quasipolynomial
2919 accordingly. This means that the C<set> passed to C<fn>
2920 will not have any existentially quantified variables, but that
2921 the dimensions of the sets may be different for different
2922 invocations of C<fn>.
2924 To iterate over all terms in a quasipolynomial,
2927 int isl_qpolynomial_foreach_term(
2928 __isl_keep isl_qpolynomial *qp,
2929 int (*fn)(__isl_take isl_term *term,
2930 void *user), void *user);
2932 The terms themselves can be inspected and freed using
2935 unsigned isl_term_dim(__isl_keep isl_term *term,
2936 enum isl_dim_type type);
2937 void isl_term_get_num(__isl_keep isl_term *term,
2939 void isl_term_get_den(__isl_keep isl_term *term,
2941 int isl_term_get_exp(__isl_keep isl_term *term,
2942 enum isl_dim_type type, unsigned pos);
2943 __isl_give isl_div *isl_term_get_div(
2944 __isl_keep isl_term *term, unsigned pos);
2945 void isl_term_free(__isl_take isl_term *term);
2947 Each term is a product of parameters, set variables and
2948 integer divisions. The function C<isl_term_get_exp>
2949 returns the exponent of a given dimensions in the given term.
2950 The C<isl_int>s in the arguments of C<isl_term_get_num>
2951 and C<isl_term_get_den> need to have been initialized
2952 using C<isl_int_init> before calling these functions.
2954 =head3 Properties of (Piecewise) Quasipolynomials
2956 To check whether a quasipolynomial is actually a constant,
2957 use the following function.
2959 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2960 isl_int *n, isl_int *d);
2962 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2963 then the numerator and denominator of the constant
2964 are returned in C<*n> and C<*d>, respectively.
2966 =head3 Operations on (Piecewise) Quasipolynomials
2968 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2969 __isl_take isl_qpolynomial *qp, isl_int v);
2970 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2971 __isl_take isl_qpolynomial *qp);
2972 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2973 __isl_take isl_qpolynomial *qp1,
2974 __isl_take isl_qpolynomial *qp2);
2975 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2976 __isl_take isl_qpolynomial *qp1,
2977 __isl_take isl_qpolynomial *qp2);
2978 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2979 __isl_take isl_qpolynomial *qp1,
2980 __isl_take isl_qpolynomial *qp2);
2981 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2982 __isl_take isl_qpolynomial *qp, unsigned exponent);
2984 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2985 __isl_take isl_pw_qpolynomial *pwqp1,
2986 __isl_take isl_pw_qpolynomial *pwqp2);
2987 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2988 __isl_take isl_pw_qpolynomial *pwqp1,
2989 __isl_take isl_pw_qpolynomial *pwqp2);
2990 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2991 __isl_take isl_pw_qpolynomial *pwqp1,
2992 __isl_take isl_pw_qpolynomial *pwqp2);
2993 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2994 __isl_take isl_pw_qpolynomial *pwqp);
2995 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2996 __isl_take isl_pw_qpolynomial *pwqp1,
2997 __isl_take isl_pw_qpolynomial *pwqp2);
2998 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
2999 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3001 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3002 __isl_take isl_union_pw_qpolynomial *upwqp1,
3003 __isl_take isl_union_pw_qpolynomial *upwqp2);
3004 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3005 __isl_take isl_union_pw_qpolynomial *upwqp1,
3006 __isl_take isl_union_pw_qpolynomial *upwqp2);
3007 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3008 __isl_take isl_union_pw_qpolynomial *upwqp1,
3009 __isl_take isl_union_pw_qpolynomial *upwqp2);
3011 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3012 __isl_take isl_pw_qpolynomial *pwqp,
3013 __isl_take isl_point *pnt);
3015 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3016 __isl_take isl_union_pw_qpolynomial *upwqp,
3017 __isl_take isl_point *pnt);
3019 __isl_give isl_set *isl_pw_qpolynomial_domain(
3020 __isl_take isl_pw_qpolynomial *pwqp);
3021 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3022 __isl_take isl_pw_qpolynomial *pwpq,
3023 __isl_take isl_set *set);
3025 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3026 __isl_take isl_union_pw_qpolynomial *upwqp);
3027 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3028 __isl_take isl_union_pw_qpolynomial *upwpq,
3029 __isl_take isl_union_set *uset);
3031 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3032 __isl_take isl_qpolynomial *qp,
3033 __isl_take isl_dim *model);
3035 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3036 __isl_take isl_union_pw_qpolynomial *upwqp);
3038 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3039 __isl_take isl_qpolynomial *qp,
3040 __isl_take isl_set *context);
3042 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3043 __isl_take isl_pw_qpolynomial *pwqp,
3044 __isl_take isl_set *context);
3046 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3047 __isl_take isl_union_pw_qpolynomial *upwqp,
3048 __isl_take isl_union_set *context);
3050 The gist operation applies the gist operation to each of
3051 the cells in the domain of the input piecewise quasipolynomial.
3052 The context is also exploited
3053 to simplify the quasipolynomials associated to each cell.
3055 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3056 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3057 __isl_give isl_union_pw_qpolynomial *
3058 isl_union_pw_qpolynomial_to_polynomial(
3059 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3061 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3062 the polynomial will be an overapproximation. If C<sign> is negative,
3063 it will be an underapproximation. If C<sign> is zero, the approximation
3064 will lie somewhere in between.
3066 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3068 A piecewise quasipolynomial reduction is a piecewise
3069 reduction (or fold) of quasipolynomials.
3070 In particular, the reduction can be maximum or a minimum.
3071 The objects are mainly used to represent the result of
3072 an upper or lower bound on a quasipolynomial over its domain,
3073 i.e., as the result of the following function.
3075 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3076 __isl_take isl_pw_qpolynomial *pwqp,
3077 enum isl_fold type, int *tight);
3079 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3080 __isl_take isl_union_pw_qpolynomial *upwqp,
3081 enum isl_fold type, int *tight);
3083 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3084 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3085 is the returned bound is known be tight, i.e., for each value
3086 of the parameters there is at least
3087 one element in the domain that reaches the bound.
3088 If the domain of C<pwqp> is not wrapping, then the bound is computed
3089 over all elements in that domain and the result has a purely parametric
3090 domain. If the domain of C<pwqp> is wrapping, then the bound is
3091 computed over the range of the wrapped relation. The domain of the
3092 wrapped relation becomes the domain of the result.
3094 A (piecewise) quasipolynomial reduction can be copied or freed using the
3095 following functions.
3097 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3098 __isl_keep isl_qpolynomial_fold *fold);
3099 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3100 __isl_keep isl_pw_qpolynomial_fold *pwf);
3101 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3102 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3103 void isl_qpolynomial_fold_free(
3104 __isl_take isl_qpolynomial_fold *fold);
3105 void *isl_pw_qpolynomial_fold_free(
3106 __isl_take isl_pw_qpolynomial_fold *pwf);
3107 void isl_union_pw_qpolynomial_fold_free(
3108 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3110 =head3 Printing Piecewise Quasipolynomial Reductions
3112 Piecewise quasipolynomial reductions can be printed
3113 using the following function.
3115 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3116 __isl_take isl_printer *p,
3117 __isl_keep isl_pw_qpolynomial_fold *pwf);
3118 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3119 __isl_take isl_printer *p,
3120 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3122 For C<isl_printer_print_pw_qpolynomial_fold>,
3123 output format of the printer
3124 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3125 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3126 output format of the printer
3127 needs to be set to C<ISL_FORMAT_ISL>.
3128 In case of printing in C<ISL_FORMAT_C>, the user may want
3129 to set the names of all dimensions
3131 __isl_give isl_pw_qpolynomial_fold *
3132 isl_pw_qpolynomial_fold_set_dim_name(
3133 __isl_take isl_pw_qpolynomial_fold *pwf,
3134 enum isl_dim_type type, unsigned pos,
3137 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3139 To iterate over all piecewise quasipolynomial reductions in a union
3140 piecewise quasipolynomial reduction, use the following function
3142 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3143 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3144 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3145 void *user), void *user);
3147 To iterate over the cells in a piecewise quasipolynomial reduction,
3148 use either of the following two functions
3150 int isl_pw_qpolynomial_fold_foreach_piece(
3151 __isl_keep isl_pw_qpolynomial_fold *pwf,
3152 int (*fn)(__isl_take isl_set *set,
3153 __isl_take isl_qpolynomial_fold *fold,
3154 void *user), void *user);
3155 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3156 __isl_keep isl_pw_qpolynomial_fold *pwf,
3157 int (*fn)(__isl_take isl_set *set,
3158 __isl_take isl_qpolynomial_fold *fold,
3159 void *user), void *user);
3161 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3162 of the difference between these two functions.
3164 To iterate over all quasipolynomials in a reduction, use
3166 int isl_qpolynomial_fold_foreach_qpolynomial(
3167 __isl_keep isl_qpolynomial_fold *fold,
3168 int (*fn)(__isl_take isl_qpolynomial *qp,
3169 void *user), void *user);
3171 =head3 Operations on Piecewise Quasipolynomial Reductions
3173 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3174 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3176 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3177 __isl_take isl_pw_qpolynomial_fold *pwf1,
3178 __isl_take isl_pw_qpolynomial_fold *pwf2);
3180 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3181 __isl_take isl_pw_qpolynomial_fold *pwf1,
3182 __isl_take isl_pw_qpolynomial_fold *pwf2);
3184 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3185 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3186 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3188 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3189 __isl_take isl_pw_qpolynomial_fold *pwf,
3190 __isl_take isl_point *pnt);
3192 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3193 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3194 __isl_take isl_point *pnt);
3196 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3197 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3198 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3199 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3200 __isl_take isl_union_set *uset);
3202 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3203 __isl_take isl_pw_qpolynomial_fold *pwf);
3205 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3206 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3208 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3209 __isl_take isl_pw_qpolynomial_fold *pwf,
3210 __isl_take isl_set *context);
3212 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3213 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3214 __isl_take isl_union_set *context);
3216 The gist operation applies the gist operation to each of
3217 the cells in the domain of the input piecewise quasipolynomial reduction.
3218 In future, the operation will also exploit the context
3219 to simplify the quasipolynomial reductions associated to each cell.
3221 __isl_give isl_pw_qpolynomial_fold *
3222 isl_set_apply_pw_qpolynomial_fold(
3223 __isl_take isl_set *set,
3224 __isl_take isl_pw_qpolynomial_fold *pwf,
3226 __isl_give isl_pw_qpolynomial_fold *
3227 isl_map_apply_pw_qpolynomial_fold(
3228 __isl_take isl_map *map,
3229 __isl_take isl_pw_qpolynomial_fold *pwf,
3231 __isl_give isl_union_pw_qpolynomial_fold *
3232 isl_union_set_apply_union_pw_qpolynomial_fold(
3233 __isl_take isl_union_set *uset,
3234 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3236 __isl_give isl_union_pw_qpolynomial_fold *
3237 isl_union_map_apply_union_pw_qpolynomial_fold(
3238 __isl_take isl_union_map *umap,
3239 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3242 The functions taking a map
3243 compose the given map with the given piecewise quasipolynomial reduction.
3244 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3245 over all elements in the intersection of the range of the map
3246 and the domain of the piecewise quasipolynomial reduction
3247 as a function of an element in the domain of the map.
3248 The functions taking a set compute a bound over all elements in the
3249 intersection of the set and the domain of the
3250 piecewise quasipolynomial reduction.
3252 =head2 Dependence Analysis
3254 C<isl> contains specialized functionality for performing
3255 array dataflow analysis. That is, given a I<sink> access relation
3256 and a collection of possible I<source> access relations,
3257 C<isl> can compute relations that describe
3258 for each iteration of the sink access, which iteration
3259 of which of the source access relations was the last
3260 to access the same data element before the given iteration
3262 To compute standard flow dependences, the sink should be
3263 a read, while the sources should be writes.
3264 If any of the source accesses are marked as being I<may>
3265 accesses, then there will be a dependence to the last
3266 I<must> access B<and> to any I<may> access that follows
3267 this last I<must> access.
3268 In particular, if I<all> sources are I<may> accesses,
3269 then memory based dependence analysis is performed.
3270 If, on the other hand, all sources are I<must> accesses,
3271 then value based dependence analysis is performed.
3273 #include <isl/flow.h>
3275 typedef int (*isl_access_level_before)(void *first, void *second);
3277 __isl_give isl_access_info *isl_access_info_alloc(
3278 __isl_take isl_map *sink,
3279 void *sink_user, isl_access_level_before fn,
3281 __isl_give isl_access_info *isl_access_info_add_source(
3282 __isl_take isl_access_info *acc,
3283 __isl_take isl_map *source, int must,
3285 void isl_access_info_free(__isl_take isl_access_info *acc);
3287 __isl_give isl_flow *isl_access_info_compute_flow(
3288 __isl_take isl_access_info *acc);
3290 int isl_flow_foreach(__isl_keep isl_flow *deps,
3291 int (*fn)(__isl_take isl_map *dep, int must,
3292 void *dep_user, void *user),
3294 __isl_give isl_map *isl_flow_get_no_source(
3295 __isl_keep isl_flow *deps, int must);
3296 void isl_flow_free(__isl_take isl_flow *deps);
3298 The function C<isl_access_info_compute_flow> performs the actual
3299 dependence analysis. The other functions are used to construct
3300 the input for this function or to read off the output.
3302 The input is collected in an C<isl_access_info>, which can
3303 be created through a call to C<isl_access_info_alloc>.
3304 The arguments to this functions are the sink access relation
3305 C<sink>, a token C<sink_user> used to identify the sink
3306 access to the user, a callback function for specifying the
3307 relative order of source and sink accesses, and the number
3308 of source access relations that will be added.
3309 The callback function has type C<int (*)(void *first, void *second)>.
3310 The function is called with two user supplied tokens identifying
3311 either a source or the sink and it should return the shared nesting
3312 level and the relative order of the two accesses.
3313 In particular, let I<n> be the number of loops shared by
3314 the two accesses. If C<first> precedes C<second> textually,
3315 then the function should return I<2 * n + 1>; otherwise,
3316 it should return I<2 * n>.
3317 The sources can be added to the C<isl_access_info> by performing
3318 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3319 C<must> indicates whether the source is a I<must> access
3320 or a I<may> access. Note that a multi-valued access relation
3321 should only be marked I<must> if every iteration in the domain
3322 of the relation accesses I<all> elements in its image.
3323 The C<source_user> token is again used to identify
3324 the source access. The range of the source access relation
3325 C<source> should have the same dimension as the range
3326 of the sink access relation.
3327 The C<isl_access_info_free> function should usually not be
3328 called explicitly, because it is called implicitly by
3329 C<isl_access_info_compute_flow>.
3331 The result of the dependence analysis is collected in an
3332 C<isl_flow>. There may be elements of
3333 the sink access for which no preceding source access could be
3334 found or for which all preceding sources are I<may> accesses.
3335 The relations containing these elements can be obtained through
3336 calls to C<isl_flow_get_no_source>, the first with C<must> set
3337 and the second with C<must> unset.
3338 In the case of standard flow dependence analysis,
3339 with the sink a read and the sources I<must> writes,
3340 the first relation corresponds to the reads from uninitialized
3341 array elements and the second relation is empty.
3342 The actual flow dependences can be extracted using
3343 C<isl_flow_foreach>. This function will call the user-specified
3344 callback function C<fn> for each B<non-empty> dependence between
3345 a source and the sink. The callback function is called
3346 with four arguments, the actual flow dependence relation
3347 mapping source iterations to sink iterations, a boolean that
3348 indicates whether it is a I<must> or I<may> dependence, a token
3349 identifying the source and an additional C<void *> with value
3350 equal to the third argument of the C<isl_flow_foreach> call.
3351 A dependence is marked I<must> if it originates from a I<must>
3352 source and if it is not followed by any I<may> sources.
3354 After finishing with an C<isl_flow>, the user should call
3355 C<isl_flow_free> to free all associated memory.
3357 A higher-level interface to dependence analysis is provided
3358 by the following function.
3360 #include <isl/flow.h>
3362 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3363 __isl_take isl_union_map *must_source,
3364 __isl_take isl_union_map *may_source,
3365 __isl_take isl_union_map *schedule,
3366 __isl_give isl_union_map **must_dep,
3367 __isl_give isl_union_map **may_dep,
3368 __isl_give isl_union_map **must_no_source,
3369 __isl_give isl_union_map **may_no_source);
3371 The arrays are identified by the tuple names of the ranges
3372 of the accesses. The iteration domains by the tuple names
3373 of the domains of the accesses and of the schedule.
3374 The relative order of the iteration domains is given by the
3375 schedule. The relations returned through C<must_no_source>
3376 and C<may_no_source> are subsets of C<sink>.
3377 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3378 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3379 any of the other arguments is treated as an error.
3383 B<The functionality described in this section is fairly new
3384 and may be subject to change.>
3386 The following function can be used to compute a schedule
3387 for a union of domains. The generated schedule respects
3388 all C<validity> dependences. That is, all dependence distances
3389 over these dependences in the scheduled space are lexicographically
3390 positive. The generated schedule schedule also tries to minimize
3391 the dependence distances over C<proximity> dependences.
3392 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3393 for groups of domains where the dependence distances have only
3394 non-negative values.
3395 The algorithm used to construct the schedule is similar to that
3398 #include <isl/schedule.h>
3399 __isl_give isl_schedule *isl_union_set_compute_schedule(
3400 __isl_take isl_union_set *domain,
3401 __isl_take isl_union_map *validity,
3402 __isl_take isl_union_map *proximity);
3403 void *isl_schedule_free(__isl_take isl_schedule *sched);
3405 A mapping from the domains to the scheduled space can be obtained
3406 from an C<isl_schedule> using the following function.
3408 __isl_give isl_union_map *isl_schedule_get_map(
3409 __isl_keep isl_schedule *sched);
3411 A representation of the schedule can be printed using
3413 __isl_give isl_printer *isl_printer_print_schedule(
3414 __isl_take isl_printer *p,
3415 __isl_keep isl_schedule *schedule);
3417 A representation of the schedule as a forest of bands can be obtained
3418 using the following function.
3420 __isl_give isl_band_list *isl_schedule_get_band_forest(
3421 __isl_keep isl_schedule *schedule);
3423 The list can be manipulated as explained in L<"Lists">.
3424 The bands inside the list can be copied and freed using the following
3427 #include <isl/band.h>
3428 __isl_give isl_band *isl_band_copy(
3429 __isl_keep isl_band *band);
3430 void *isl_band_free(__isl_take isl_band *band);
3432 Each band contains zero or more scheduling dimensions.
3433 These are referred to as the members of the band.
3434 The section of the schedule that corresponds to the band is
3435 referred to as the partial schedule of the band.
3436 For those nodes that participate in a band, the outer scheduling
3437 dimensions form the prefix schedule, while the inner scheduling
3438 dimensions form the suffix schedule.
3439 That is, if we take a cut of the band forest, then the union of
3440 the concatenations of the prefix, partial and suffix schedules of
3441 each band in the cut is equal to the entire schedule (modulo
3442 some possible padding at the end with zero scheduling dimensions).
3443 The properties of a band can be inspected using the following functions.
3445 #include <isl/band.h>
3446 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3448 int isl_band_has_children(__isl_keep isl_band *band);
3449 __isl_give isl_band_list *isl_band_get_children(
3450 __isl_keep isl_band *band);
3452 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3453 __isl_keep isl_band *band);
3454 __isl_give isl_union_map *isl_band_get_partial_schedule(
3455 __isl_keep isl_band *band);
3456 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3457 __isl_keep isl_band *band);
3459 int isl_band_n_member(__isl_keep isl_band *band);
3460 int isl_band_member_is_zero_distance(
3461 __isl_keep isl_band *band, int pos);
3463 Note that a scheduling dimension is considered to be ``zero
3464 distance'' if it does not carry any proximity dependences
3466 That is, if the dependence distances of the proximity
3467 dependences are all zero in that direction (for fixed
3468 iterations of outer bands).
3470 A representation of the band can be printed using
3472 #include <isl/band.h>
3473 __isl_give isl_printer *isl_printer_print_band(
3474 __isl_take isl_printer *p,
3475 __isl_keep isl_band *band);
3477 =head2 Parametric Vertex Enumeration
3479 The parametric vertex enumeration described in this section
3480 is mainly intended to be used internally and by the C<barvinok>
3483 #include <isl/vertices.h>
3484 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3485 __isl_keep isl_basic_set *bset);
3487 The function C<isl_basic_set_compute_vertices> performs the
3488 actual computation of the parametric vertices and the chamber
3489 decomposition and store the result in an C<isl_vertices> object.
3490 This information can be queried by either iterating over all
3491 the vertices or iterating over all the chambers or cells
3492 and then iterating over all vertices that are active on the chamber.
3494 int isl_vertices_foreach_vertex(
3495 __isl_keep isl_vertices *vertices,
3496 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3499 int isl_vertices_foreach_cell(
3500 __isl_keep isl_vertices *vertices,
3501 int (*fn)(__isl_take isl_cell *cell, void *user),
3503 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3504 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3507 Other operations that can be performed on an C<isl_vertices> object are
3510 isl_ctx *isl_vertices_get_ctx(
3511 __isl_keep isl_vertices *vertices);
3512 int isl_vertices_get_n_vertices(
3513 __isl_keep isl_vertices *vertices);
3514 void isl_vertices_free(__isl_take isl_vertices *vertices);
3516 Vertices can be inspected and destroyed using the following functions.
3518 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3519 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3520 __isl_give isl_basic_set *isl_vertex_get_domain(
3521 __isl_keep isl_vertex *vertex);
3522 __isl_give isl_basic_set *isl_vertex_get_expr(
3523 __isl_keep isl_vertex *vertex);
3524 void isl_vertex_free(__isl_take isl_vertex *vertex);
3526 C<isl_vertex_get_expr> returns a singleton parametric set describing
3527 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3529 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3530 B<rational> basic sets, so they should mainly be used for inspection
3531 and should not be mixed with integer sets.
3533 Chambers can be inspected and destroyed using the following functions.
3535 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3536 __isl_give isl_basic_set *isl_cell_get_domain(
3537 __isl_keep isl_cell *cell);
3538 void isl_cell_free(__isl_take isl_cell *cell);
3542 Although C<isl> is mainly meant to be used as a library,
3543 it also contains some basic applications that use some
3544 of the functionality of C<isl>.
3545 The input may be specified in either the L<isl format>
3546 or the L<PolyLib format>.
3548 =head2 C<isl_polyhedron_sample>
3550 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3551 an integer element of the polyhedron, if there is any.
3552 The first column in the output is the denominator and is always
3553 equal to 1. If the polyhedron contains no integer points,
3554 then a vector of length zero is printed.
3558 C<isl_pip> takes the same input as the C<example> program
3559 from the C<piplib> distribution, i.e., a set of constraints
3560 on the parameters, a line containing only -1 and finally a set
3561 of constraints on a parametric polyhedron.
3562 The coefficients of the parameters appear in the last columns
3563 (but before the final constant column).
3564 The output is the lexicographic minimum of the parametric polyhedron.
3565 As C<isl> currently does not have its own output format, the output
3566 is just a dump of the internal state.
3568 =head2 C<isl_polyhedron_minimize>
3570 C<isl_polyhedron_minimize> computes the minimum of some linear
3571 or affine objective function over the integer points in a polyhedron.
3572 If an affine objective function
3573 is given, then the constant should appear in the last column.
3575 =head2 C<isl_polytope_scan>
3577 Given a polytope, C<isl_polytope_scan> prints
3578 all integer points in the polytope.