3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
90 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
91 Some of the old names have been kept for backward compatibility,
92 but they will be removed in the future.
96 =head3 Changes since isl-0.07
100 =item * The function C<isl_pw_aff_max> has been renamed to
101 C<isl_pw_aff_union_max>.
107 The source of C<isl> can be obtained either as a tarball
108 or from the git repository. Both are available from
109 L<http://freshmeat.net/projects/isl/>.
110 The installation process depends on how you obtained
113 =head2 Installation from the git repository
117 =item 1 Clone or update the repository
119 The first time the source is obtained, you need to clone
122 git clone git://repo.or.cz/isl.git
124 To obtain updates, you need to pull in the latest changes
128 =item 2 Generate C<configure>
134 After performing the above steps, continue
135 with the L<Common installation instructions>.
137 =head2 Common installation instructions
141 =item 1 Obtain C<GMP>
143 Building C<isl> requires C<GMP>, including its headers files.
144 Your distribution may not provide these header files by default
145 and you may need to install a package called C<gmp-devel> or something
146 similar. Alternatively, C<GMP> can be built from
147 source, available from L<http://gmplib.org/>.
151 C<isl> uses the standard C<autoconf> C<configure> script.
156 optionally followed by some configure options.
157 A complete list of options can be obtained by running
161 Below we discuss some of the more common options.
163 C<isl> can optionally use C<piplib>, but no
164 C<piplib> functionality is currently used by default.
165 The C<--with-piplib> option can
166 be used to specify which C<piplib>
167 library to use, either an installed version (C<system>),
168 an externally built version (C<build>)
169 or no version (C<no>). The option C<build> is mostly useful
170 in C<configure> scripts of larger projects that bundle both C<isl>
177 Installation prefix for C<isl>
179 =item C<--with-gmp-prefix>
181 Installation prefix for C<GMP> (architecture-independent files).
183 =item C<--with-gmp-exec-prefix>
185 Installation prefix for C<GMP> (architecture-dependent files).
187 =item C<--with-piplib>
189 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
191 =item C<--with-piplib-prefix>
193 Installation prefix for C<system> C<piplib> (architecture-independent files).
195 =item C<--with-piplib-exec-prefix>
197 Installation prefix for C<system> C<piplib> (architecture-dependent files).
199 =item C<--with-piplib-builddir>
201 Location where C<build> C<piplib> was built.
209 =item 4 Install (optional)
217 =head2 Initialization
219 All manipulations of integer sets and relations occur within
220 the context of an C<isl_ctx>.
221 A given C<isl_ctx> can only be used within a single thread.
222 All arguments of a function are required to have been allocated
223 within the same context.
224 There are currently no functions available for moving an object
225 from one C<isl_ctx> to another C<isl_ctx>. This means that
226 there is currently no way of safely moving an object from one
227 thread to another, unless the whole C<isl_ctx> is moved.
229 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
230 freed using C<isl_ctx_free>.
231 All objects allocated within an C<isl_ctx> should be freed
232 before the C<isl_ctx> itself is freed.
234 isl_ctx *isl_ctx_alloc();
235 void isl_ctx_free(isl_ctx *ctx);
239 All operations on integers, mainly the coefficients
240 of the constraints describing the sets and relations,
241 are performed in exact integer arithmetic using C<GMP>.
242 However, to allow future versions of C<isl> to optionally
243 support fixed integer arithmetic, all calls to C<GMP>
244 are wrapped inside C<isl> specific macros.
245 The basic type is C<isl_int> and the operations below
246 are available on this type.
247 The meanings of these operations are essentially the same
248 as their C<GMP> C<mpz_> counterparts.
249 As always with C<GMP> types, C<isl_int>s need to be
250 initialized with C<isl_int_init> before they can be used
251 and they need to be released with C<isl_int_clear>
253 The user should not assume that an C<isl_int> is represented
254 as a C<mpz_t>, but should instead explicitly convert between
255 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
256 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
260 =item isl_int_init(i)
262 =item isl_int_clear(i)
264 =item isl_int_set(r,i)
266 =item isl_int_set_si(r,i)
268 =item isl_int_set_gmp(r,g)
270 =item isl_int_get_gmp(i,g)
272 =item isl_int_abs(r,i)
274 =item isl_int_neg(r,i)
276 =item isl_int_swap(i,j)
278 =item isl_int_swap_or_set(i,j)
280 =item isl_int_add_ui(r,i,j)
282 =item isl_int_sub_ui(r,i,j)
284 =item isl_int_add(r,i,j)
286 =item isl_int_sub(r,i,j)
288 =item isl_int_mul(r,i,j)
290 =item isl_int_mul_ui(r,i,j)
292 =item isl_int_addmul(r,i,j)
294 =item isl_int_submul(r,i,j)
296 =item isl_int_gcd(r,i,j)
298 =item isl_int_lcm(r,i,j)
300 =item isl_int_divexact(r,i,j)
302 =item isl_int_cdiv_q(r,i,j)
304 =item isl_int_fdiv_q(r,i,j)
306 =item isl_int_fdiv_r(r,i,j)
308 =item isl_int_fdiv_q_ui(r,i,j)
310 =item isl_int_read(r,s)
312 =item isl_int_print(out,i,width)
316 =item isl_int_cmp(i,j)
318 =item isl_int_cmp_si(i,si)
320 =item isl_int_eq(i,j)
322 =item isl_int_ne(i,j)
324 =item isl_int_lt(i,j)
326 =item isl_int_le(i,j)
328 =item isl_int_gt(i,j)
330 =item isl_int_ge(i,j)
332 =item isl_int_abs_eq(i,j)
334 =item isl_int_abs_ne(i,j)
336 =item isl_int_abs_lt(i,j)
338 =item isl_int_abs_gt(i,j)
340 =item isl_int_abs_ge(i,j)
342 =item isl_int_is_zero(i)
344 =item isl_int_is_one(i)
346 =item isl_int_is_negone(i)
348 =item isl_int_is_pos(i)
350 =item isl_int_is_neg(i)
352 =item isl_int_is_nonpos(i)
354 =item isl_int_is_nonneg(i)
356 =item isl_int_is_divisible_by(i,j)
360 =head2 Sets and Relations
362 C<isl> uses six types of objects for representing sets and relations,
363 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
364 C<isl_union_set> and C<isl_union_map>.
365 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
366 can be described as a conjunction of affine constraints, while
367 C<isl_set> and C<isl_map> represent unions of
368 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
369 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
370 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
371 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
372 where dimensions with different space names
373 (see L<Dimension Specifications>) are considered different as well.
374 The difference between sets and relations (maps) is that sets have
375 one set of variables, while relations have two sets of variables,
376 input variables and output variables.
378 =head2 Memory Management
380 Since a high-level operation on sets and/or relations usually involves
381 several substeps and since the user is usually not interested in
382 the intermediate results, most functions that return a new object
383 will also release all the objects passed as arguments.
384 If the user still wants to use one or more of these arguments
385 after the function call, she should pass along a copy of the
386 object rather than the object itself.
387 The user is then responsible for making sure that the original
388 object gets used somewhere else or is explicitly freed.
390 The arguments and return values of all documented functions are
391 annotated to make clear which arguments are released and which
392 arguments are preserved. In particular, the following annotations
399 C<__isl_give> means that a new object is returned.
400 The user should make sure that the returned pointer is
401 used exactly once as a value for an C<__isl_take> argument.
402 In between, it can be used as a value for as many
403 C<__isl_keep> arguments as the user likes.
404 There is one exception, and that is the case where the
405 pointer returned is C<NULL>. Is this case, the user
406 is free to use it as an C<__isl_take> argument or not.
410 C<__isl_take> means that the object the argument points to
411 is taken over by the function and may no longer be used
412 by the user as an argument to any other function.
413 The pointer value must be one returned by a function
414 returning an C<__isl_give> pointer.
415 If the user passes in a C<NULL> value, then this will
416 be treated as an error in the sense that the function will
417 not perform its usual operation. However, it will still
418 make sure that all the other C<__isl_take> arguments
423 C<__isl_keep> means that the function will only use the object
424 temporarily. After the function has finished, the user
425 can still use it as an argument to other functions.
426 A C<NULL> value will be treated in the same way as
427 a C<NULL> value for an C<__isl_take> argument.
433 Identifiers are used to identify both individual dimensions
434 and tuples of dimensions. They consist of a name and an optional
435 pointer. Identifiers with the same name but different pointer values
436 are considered to be distinct.
437 Identifiers can be constructed, copied, freed, inspected and printed
438 using the following functions.
441 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
442 __isl_keep const char *name, void *user);
443 __isl_give isl_id *isl_id_copy(isl_id *id);
444 void *isl_id_free(__isl_take isl_id *id);
446 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
447 void *isl_id_get_user(__isl_keep isl_id *id);
448 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
450 __isl_give isl_printer *isl_printer_print_id(
451 __isl_take isl_printer *p, __isl_keep isl_id *id);
453 Note that C<isl_id_get_name> returns a pointer to some internal
454 data structure, so the result can only be used while the
455 corresponding C<isl_id> is alive.
457 =head2 Dimension Specifications
459 Whenever a new set or relation is created from scratch,
460 its dimension needs to be specified using an C<isl_dim>.
463 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
464 unsigned nparam, unsigned n_in, unsigned n_out);
465 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
466 unsigned nparam, unsigned dim);
467 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
468 void isl_dim_free(__isl_take isl_dim *dim);
469 unsigned isl_dim_size(__isl_keep isl_dim *dim,
470 enum isl_dim_type type);
472 The dimension specification used for creating a set
473 needs to be created using C<isl_dim_set_alloc>, while
474 that for creating a relation
475 needs to be created using C<isl_dim_alloc>.
476 C<isl_dim_size> can be used
477 to find out the number of dimensions of each type in
478 a dimension specification, where type may be
479 C<isl_dim_param>, C<isl_dim_in> (only for relations),
480 C<isl_dim_out> (only for relations), C<isl_dim_set>
481 (only for sets) or C<isl_dim_all>.
483 It is often useful to create objects that live in the
484 same space as some other object. This can be accomplished
485 by creating the new objects
486 (see L<Creating New Sets and Relations> or
487 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
488 specification of the original object.
491 __isl_give isl_dim *isl_basic_set_get_dim(
492 __isl_keep isl_basic_set *bset);
493 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
495 #include <isl/union_set.h>
496 __isl_give isl_dim *isl_union_set_get_dim(
497 __isl_keep isl_union_set *uset);
500 __isl_give isl_dim *isl_basic_map_get_dim(
501 __isl_keep isl_basic_map *bmap);
502 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
504 #include <isl/union_map.h>
505 __isl_give isl_dim *isl_union_map_get_dim(
506 __isl_keep isl_union_map *umap);
508 #include <isl/constraint.h>
509 __isl_give isl_dim *isl_constraint_get_dim(
510 __isl_keep isl_constraint *constraint);
512 #include <isl/polynomial.h>
513 __isl_give isl_dim *isl_qpolynomial_get_dim(
514 __isl_keep isl_qpolynomial *qp);
515 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
516 __isl_keep isl_qpolynomial_fold *fold);
517 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
518 __isl_keep isl_pw_qpolynomial *pwqp);
519 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
520 __isl_keep isl_union_pw_qpolynomial *upwqp);
521 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
522 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
525 __isl_give isl_dim *isl_aff_get_dim(
526 __isl_keep isl_aff *aff);
527 __isl_give isl_dim *isl_pw_aff_get_dim(
528 __isl_keep isl_pw_aff *pwaff);
530 #include <isl/point.h>
531 __isl_give isl_dim *isl_point_get_dim(
532 __isl_keep isl_point *pnt);
534 The identifiers or names of the individual dimensions may be set or read off
535 using the following functions.
538 __isl_give isl_dim *isl_dim_set_dim_id(
539 __isl_take isl_dim *dim,
540 enum isl_dim_type type, unsigned pos,
541 __isl_take isl_id *id);
542 __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 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 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 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.
1058 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 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(__isl_take 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 The number of parameters, input, output or set dimensions can
1308 be obtained using the following functions.
1310 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1311 enum isl_dim_type type);
1312 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1313 enum isl_dim_type type);
1314 unsigned isl_set_dim(__isl_keep isl_set *set,
1315 enum isl_dim_type type);
1316 unsigned isl_map_dim(__isl_keep isl_map *map,
1317 enum isl_dim_type type);
1319 To check whether the description of a set or relation depends
1320 on one or more given dimensions, it is not necessary to iterate over all
1321 constraints. Instead the following functions can be used.
1323 int isl_basic_set_involves_dims(
1324 __isl_keep isl_basic_set *bset,
1325 enum isl_dim_type type, unsigned first, unsigned n);
1326 int isl_set_involves_dims(__isl_keep isl_set *set,
1327 enum isl_dim_type type, unsigned first, unsigned n);
1328 int isl_basic_map_involves_dims(
1329 __isl_keep isl_basic_map *bmap,
1330 enum isl_dim_type type, unsigned first, unsigned n);
1331 int isl_map_involves_dims(__isl_keep isl_map *map,
1332 enum isl_dim_type type, unsigned first, unsigned n);
1334 Similarly, the following functions can be used to check whether
1335 a given dimension is involved in any lower or upper bound.
1337 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1338 enum isl_dim_type type, unsigned pos);
1339 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1340 enum isl_dim_type type, unsigned pos);
1342 The identifiers or names of the domain and range spaces of a set
1343 or relation can be read off or set using the following functions.
1345 __isl_give isl_set *isl_set_set_tuple_id(
1346 __isl_take isl_set *set, __isl_take isl_id *id);
1347 __isl_give isl_set *isl_set_reset_tuple_id(
1348 __isl_take isl_set *set);
1349 __isl_give isl_id *isl_set_get_tuple_id(
1350 __isl_keep isl_set *set);
1351 __isl_give isl_map *isl_map_set_tuple_id(
1352 __isl_take isl_map *map, enum isl_dim_type type,
1353 __isl_take isl_id *id);
1354 __isl_give isl_map *isl_map_reset_tuple_id(
1355 __isl_take isl_map *map, enum isl_dim_type type);
1356 __isl_give isl_id *isl_map_get_tuple_id(
1357 __isl_keep isl_map *map, enum isl_dim_type type);
1359 const char *isl_basic_set_get_tuple_name(
1360 __isl_keep isl_basic_set *bset);
1361 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1362 __isl_take isl_basic_set *set, const char *s);
1363 const char *isl_set_get_tuple_name(
1364 __isl_keep isl_set *set);
1365 const char *isl_basic_map_get_tuple_name(
1366 __isl_keep isl_basic_map *bmap,
1367 enum isl_dim_type type);
1368 const char *isl_map_get_tuple_name(
1369 __isl_keep isl_map *map,
1370 enum isl_dim_type type);
1372 As with C<isl_dim_get_tuple_name>, the value returned points to
1373 an internal data structure.
1374 The identifiers, positions or names of individual dimensions can be
1375 read off using the following functions.
1377 __isl_give isl_set *isl_set_set_dim_id(
1378 __isl_take isl_set *set, enum isl_dim_type type,
1379 unsigned pos, __isl_take isl_id *id);
1380 __isl_give isl_id *isl_set_get_dim_id(
1381 __isl_keep isl_set *set, enum isl_dim_type type,
1383 __isl_give isl_map *isl_map_set_dim_id(
1384 __isl_take isl_map *map, enum isl_dim_type type,
1385 unsigned pos, __isl_take isl_id *id);
1386 __isl_give isl_id *isl_map_get_dim_id(
1387 __isl_keep isl_map *map, enum isl_dim_type type,
1390 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1391 enum isl_dim_type type, __isl_keep isl_id *id);
1392 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1393 enum isl_dim_type type, __isl_keep isl_id *id);
1395 const char *isl_constraint_get_dim_name(
1396 __isl_keep isl_constraint *constraint,
1397 enum isl_dim_type type, unsigned pos);
1398 const char *isl_basic_set_get_dim_name(
1399 __isl_keep isl_basic_set *bset,
1400 enum isl_dim_type type, unsigned pos);
1401 const char *isl_set_get_dim_name(
1402 __isl_keep isl_set *set,
1403 enum isl_dim_type type, unsigned pos);
1404 const char *isl_basic_map_get_dim_name(
1405 __isl_keep isl_basic_map *bmap,
1406 enum isl_dim_type type, unsigned pos);
1407 const char *isl_map_get_dim_name(
1408 __isl_keep isl_map *map,
1409 enum isl_dim_type type, unsigned pos);
1411 These functions are mostly useful to obtain the identifiers, positions
1412 or names of the parameters. Identifiers of individual dimensions are
1413 essentially only useful for printing. They are ignored by all other
1414 operations and may not be preserved across those operations.
1418 =head3 Unary Properties
1424 The following functions test whether the given set or relation
1425 contains any integer points. The ``plain'' variants do not perform
1426 any computations, but simply check if the given set or relation
1427 is already known to be empty.
1429 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1430 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1431 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1432 int isl_set_is_empty(__isl_keep isl_set *set);
1433 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1434 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1435 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1436 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1437 int isl_map_is_empty(__isl_keep isl_map *map);
1438 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1440 =item * Universality
1442 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1443 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1444 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1446 =item * Single-valuedness
1448 int isl_map_is_single_valued(__isl_keep isl_map *map);
1449 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1453 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1454 int isl_map_is_injective(__isl_keep isl_map *map);
1455 int isl_union_map_plain_is_injective(
1456 __isl_keep isl_union_map *umap);
1457 int isl_union_map_is_injective(
1458 __isl_keep isl_union_map *umap);
1462 int isl_map_is_bijective(__isl_keep isl_map *map);
1463 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1467 int isl_basic_map_plain_is_fixed(
1468 __isl_keep isl_basic_map *bmap,
1469 enum isl_dim_type type, unsigned pos,
1471 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1472 enum isl_dim_type type, unsigned pos,
1475 Check if the relation obviously lies on a hyperplane where the given dimension
1476 has a fixed value and if so, return that value in C<*val>.
1480 The following functions check whether the domain of the given
1481 (basic) set is a wrapped relation.
1483 int isl_basic_set_is_wrapping(
1484 __isl_keep isl_basic_set *bset);
1485 int isl_set_is_wrapping(__isl_keep isl_set *set);
1487 =item * Internal Product
1489 int isl_basic_map_can_zip(
1490 __isl_keep isl_basic_map *bmap);
1491 int isl_map_can_zip(__isl_keep isl_map *map);
1493 Check whether the product of domain and range of the given relation
1495 i.e., whether both domain and range are nested relations.
1499 =head3 Binary Properties
1505 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1506 __isl_keep isl_set *set2);
1507 int isl_set_is_equal(__isl_keep isl_set *set1,
1508 __isl_keep isl_set *set2);
1509 int isl_union_set_is_equal(
1510 __isl_keep isl_union_set *uset1,
1511 __isl_keep isl_union_set *uset2);
1512 int isl_basic_map_is_equal(
1513 __isl_keep isl_basic_map *bmap1,
1514 __isl_keep isl_basic_map *bmap2);
1515 int isl_map_is_equal(__isl_keep isl_map *map1,
1516 __isl_keep isl_map *map2);
1517 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1518 __isl_keep isl_map *map2);
1519 int isl_union_map_is_equal(
1520 __isl_keep isl_union_map *umap1,
1521 __isl_keep isl_union_map *umap2);
1523 =item * Disjointness
1525 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1526 __isl_keep isl_set *set2);
1530 int isl_set_is_subset(__isl_keep isl_set *set1,
1531 __isl_keep isl_set *set2);
1532 int isl_set_is_strict_subset(
1533 __isl_keep isl_set *set1,
1534 __isl_keep isl_set *set2);
1535 int isl_union_set_is_subset(
1536 __isl_keep isl_union_set *uset1,
1537 __isl_keep isl_union_set *uset2);
1538 int isl_union_set_is_strict_subset(
1539 __isl_keep isl_union_set *uset1,
1540 __isl_keep isl_union_set *uset2);
1541 int isl_basic_map_is_subset(
1542 __isl_keep isl_basic_map *bmap1,
1543 __isl_keep isl_basic_map *bmap2);
1544 int isl_basic_map_is_strict_subset(
1545 __isl_keep isl_basic_map *bmap1,
1546 __isl_keep isl_basic_map *bmap2);
1547 int isl_map_is_subset(
1548 __isl_keep isl_map *map1,
1549 __isl_keep isl_map *map2);
1550 int isl_map_is_strict_subset(
1551 __isl_keep isl_map *map1,
1552 __isl_keep isl_map *map2);
1553 int isl_union_map_is_subset(
1554 __isl_keep isl_union_map *umap1,
1555 __isl_keep isl_union_map *umap2);
1556 int isl_union_map_is_strict_subset(
1557 __isl_keep isl_union_map *umap1,
1558 __isl_keep isl_union_map *umap2);
1562 =head2 Unary Operations
1568 __isl_give isl_set *isl_set_complement(
1569 __isl_take isl_set *set);
1573 __isl_give isl_basic_map *isl_basic_map_reverse(
1574 __isl_take isl_basic_map *bmap);
1575 __isl_give isl_map *isl_map_reverse(
1576 __isl_take isl_map *map);
1577 __isl_give isl_union_map *isl_union_map_reverse(
1578 __isl_take isl_union_map *umap);
1582 __isl_give isl_basic_set *isl_basic_set_project_out(
1583 __isl_take isl_basic_set *bset,
1584 enum isl_dim_type type, unsigned first, unsigned n);
1585 __isl_give isl_basic_map *isl_basic_map_project_out(
1586 __isl_take isl_basic_map *bmap,
1587 enum isl_dim_type type, unsigned first, unsigned n);
1588 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1589 enum isl_dim_type type, unsigned first, unsigned n);
1590 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1591 enum isl_dim_type type, unsigned first, unsigned n);
1592 __isl_give isl_basic_set *isl_basic_map_domain(
1593 __isl_take isl_basic_map *bmap);
1594 __isl_give isl_basic_set *isl_basic_map_range(
1595 __isl_take isl_basic_map *bmap);
1596 __isl_give isl_set *isl_map_domain(
1597 __isl_take isl_map *bmap);
1598 __isl_give isl_set *isl_map_range(
1599 __isl_take isl_map *map);
1600 __isl_give isl_union_set *isl_union_map_domain(
1601 __isl_take isl_union_map *umap);
1602 __isl_give isl_union_set *isl_union_map_range(
1603 __isl_take isl_union_map *umap);
1605 __isl_give isl_basic_map *isl_basic_map_domain_map(
1606 __isl_take isl_basic_map *bmap);
1607 __isl_give isl_basic_map *isl_basic_map_range_map(
1608 __isl_take isl_basic_map *bmap);
1609 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1610 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1611 __isl_give isl_union_map *isl_union_map_domain_map(
1612 __isl_take isl_union_map *umap);
1613 __isl_give isl_union_map *isl_union_map_range_map(
1614 __isl_take isl_union_map *umap);
1616 The functions above construct a (basic, regular or union) relation
1617 that maps (a wrapped version of) the input relation to its domain or range.
1621 __isl_give isl_set *isl_set_eliminate(
1622 __isl_take isl_set *set, enum isl_dim_type type,
1623 unsigned first, unsigned n);
1625 Eliminate the coefficients for the given dimensions from the constraints,
1626 without removing the dimensions.
1630 __isl_give isl_basic_set *isl_basic_set_fix(
1631 __isl_take isl_basic_set *bset,
1632 enum isl_dim_type type, unsigned pos,
1634 __isl_give isl_basic_set *isl_basic_set_fix_si(
1635 __isl_take isl_basic_set *bset,
1636 enum isl_dim_type type, unsigned pos, int value);
1637 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1638 enum isl_dim_type type, unsigned pos,
1640 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1641 enum isl_dim_type type, unsigned pos, int value);
1642 __isl_give isl_basic_map *isl_basic_map_fix_si(
1643 __isl_take isl_basic_map *bmap,
1644 enum isl_dim_type type, unsigned pos, int value);
1645 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1646 enum isl_dim_type type, unsigned pos, int value);
1648 Intersect the set or relation with the hyperplane where the given
1649 dimension has the fixed given value.
1651 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1652 enum isl_dim_type type1, int pos1,
1653 enum isl_dim_type type2, int pos2);
1654 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1655 enum isl_dim_type type1, int pos1,
1656 enum isl_dim_type type2, int pos2);
1658 Intersect the set or relation with the hyperplane where the given
1659 dimensions are equal to each other.
1661 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1662 enum isl_dim_type type1, int pos1,
1663 enum isl_dim_type type2, int pos2);
1665 Intersect the relation with the hyperplane where the given
1666 dimensions have opposite values.
1670 __isl_give isl_map *isl_set_identity(
1671 __isl_take isl_set *set);
1672 __isl_give isl_union_map *isl_union_set_identity(
1673 __isl_take isl_union_set *uset);
1675 Construct an identity relation on the given (union) set.
1679 __isl_give isl_basic_set *isl_basic_map_deltas(
1680 __isl_take isl_basic_map *bmap);
1681 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1682 __isl_give isl_union_set *isl_union_map_deltas(
1683 __isl_take isl_union_map *umap);
1685 These functions return a (basic) set containing the differences
1686 between image elements and corresponding domain elements in the input.
1688 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1689 __isl_take isl_basic_map *bmap);
1690 __isl_give isl_map *isl_map_deltas_map(
1691 __isl_take isl_map *map);
1692 __isl_give isl_union_map *isl_union_map_deltas_map(
1693 __isl_take isl_union_map *umap);
1695 The functions above construct a (basic, regular or union) relation
1696 that maps (a wrapped version of) the input relation to its delta set.
1700 Simplify the representation of a set or relation by trying
1701 to combine pairs of basic sets or relations into a single
1702 basic set or relation.
1704 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1705 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1706 __isl_give isl_union_set *isl_union_set_coalesce(
1707 __isl_take isl_union_set *uset);
1708 __isl_give isl_union_map *isl_union_map_coalesce(
1709 __isl_take isl_union_map *umap);
1711 =item * Detecting equalities
1713 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1714 __isl_take isl_basic_set *bset);
1715 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1716 __isl_take isl_basic_map *bmap);
1717 __isl_give isl_set *isl_set_detect_equalities(
1718 __isl_take isl_set *set);
1719 __isl_give isl_map *isl_map_detect_equalities(
1720 __isl_take isl_map *map);
1721 __isl_give isl_union_set *isl_union_set_detect_equalities(
1722 __isl_take isl_union_set *uset);
1723 __isl_give isl_union_map *isl_union_map_detect_equalities(
1724 __isl_take isl_union_map *umap);
1726 Simplify the representation of a set or relation by detecting implicit
1729 =item * Removing redundant constraints
1731 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1732 __isl_take isl_basic_set *bset);
1733 __isl_give isl_set *isl_set_remove_redundancies(
1734 __isl_take isl_set *set);
1735 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1736 __isl_take isl_basic_map *bmap);
1737 __isl_give isl_map *isl_map_remove_redundancies(
1738 __isl_take isl_map *map);
1742 __isl_give isl_basic_set *isl_set_convex_hull(
1743 __isl_take isl_set *set);
1744 __isl_give isl_basic_map *isl_map_convex_hull(
1745 __isl_take isl_map *map);
1747 If the input set or relation has any existentially quantified
1748 variables, then the result of these operations is currently undefined.
1752 __isl_give isl_basic_set *isl_set_simple_hull(
1753 __isl_take isl_set *set);
1754 __isl_give isl_basic_map *isl_map_simple_hull(
1755 __isl_take isl_map *map);
1756 __isl_give isl_union_map *isl_union_map_simple_hull(
1757 __isl_take isl_union_map *umap);
1759 These functions compute a single basic set or relation
1760 that contains the whole input set or relation.
1761 In particular, the output is described by translates
1762 of the constraints describing the basic sets or relations in the input.
1766 (See \autoref{s:simple hull}.)
1772 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1773 __isl_take isl_basic_set *bset);
1774 __isl_give isl_basic_set *isl_set_affine_hull(
1775 __isl_take isl_set *set);
1776 __isl_give isl_union_set *isl_union_set_affine_hull(
1777 __isl_take isl_union_set *uset);
1778 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1779 __isl_take isl_basic_map *bmap);
1780 __isl_give isl_basic_map *isl_map_affine_hull(
1781 __isl_take isl_map *map);
1782 __isl_give isl_union_map *isl_union_map_affine_hull(
1783 __isl_take isl_union_map *umap);
1785 In case of union sets and relations, the affine hull is computed
1788 =item * Polyhedral hull
1790 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1791 __isl_take isl_set *set);
1792 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1793 __isl_take isl_map *map);
1794 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1795 __isl_take isl_union_set *uset);
1796 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1797 __isl_take isl_union_map *umap);
1799 These functions compute a single basic set or relation
1800 not involving any existentially quantified variables
1801 that contains the whole input set or relation.
1802 In case of union sets and relations, the polyhedral hull is computed
1805 =item * Optimization
1807 #include <isl/ilp.h>
1808 enum isl_lp_result isl_basic_set_max(
1809 __isl_keep isl_basic_set *bset,
1810 __isl_keep isl_aff *obj, isl_int *opt)
1811 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1812 __isl_keep isl_aff *obj, isl_int *opt);
1813 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1814 __isl_keep isl_aff *obj, isl_int *opt);
1816 Compute the minimum or maximum of the integer affine expression C<obj>
1817 over the points in C<set>, returning the result in C<opt>.
1818 The return value may be one of C<isl_lp_error>,
1819 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1821 =item * Parametric optimization
1823 __isl_give isl_pw_aff *isl_set_dim_max(
1824 __isl_take isl_set *set, int pos);
1826 Compute the maximum of the given set dimension as a function of the
1827 parameters, but independently of the other set dimensions.
1828 For lexicographic optimization, see L<"Lexicographic Optimization">.
1832 The following functions compute either the set of (rational) coefficient
1833 values of valid constraints for the given set or the set of (rational)
1834 values satisfying the constraints with coefficients from the given set.
1835 Internally, these two sets of functions perform essentially the
1836 same operations, except that the set of coefficients is assumed to
1837 be a cone, while the set of values may be any polyhedron.
1838 The current implementation is based on the Farkas lemma and
1839 Fourier-Motzkin elimination, but this may change or be made optional
1840 in future. In particular, future implementations may use different
1841 dualization algorithms or skip the elimination step.
1843 __isl_give isl_basic_set *isl_basic_set_coefficients(
1844 __isl_take isl_basic_set *bset);
1845 __isl_give isl_basic_set *isl_set_coefficients(
1846 __isl_take isl_set *set);
1847 __isl_give isl_union_set *isl_union_set_coefficients(
1848 __isl_take isl_union_set *bset);
1849 __isl_give isl_basic_set *isl_basic_set_solutions(
1850 __isl_take isl_basic_set *bset);
1851 __isl_give isl_basic_set *isl_set_solutions(
1852 __isl_take isl_set *set);
1853 __isl_give isl_union_set *isl_union_set_solutions(
1854 __isl_take isl_union_set *bset);
1858 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1860 __isl_give isl_union_map *isl_union_map_power(
1861 __isl_take isl_union_map *umap, int *exact);
1863 Compute a parametric representation for all positive powers I<k> of C<map>.
1864 The result maps I<k> to a nested relation corresponding to the
1865 I<k>th power of C<map>.
1866 The result may be an overapproximation. If the result is known to be exact,
1867 then C<*exact> is set to C<1>.
1869 =item * Transitive closure
1871 __isl_give isl_map *isl_map_transitive_closure(
1872 __isl_take isl_map *map, int *exact);
1873 __isl_give isl_union_map *isl_union_map_transitive_closure(
1874 __isl_take isl_union_map *umap, int *exact);
1876 Compute the transitive closure of C<map>.
1877 The result may be an overapproximation. If the result is known to be exact,
1878 then C<*exact> is set to C<1>.
1880 =item * Reaching path lengths
1882 __isl_give isl_map *isl_map_reaching_path_lengths(
1883 __isl_take isl_map *map, int *exact);
1885 Compute a relation that maps each element in the range of C<map>
1886 to the lengths of all paths composed of edges in C<map> that
1887 end up in the given element.
1888 The result may be an overapproximation. If the result is known to be exact,
1889 then C<*exact> is set to C<1>.
1890 To compute the I<maximal> path length, the resulting relation
1891 should be postprocessed by C<isl_map_lexmax>.
1892 In particular, if the input relation is a dependence relation
1893 (mapping sources to sinks), then the maximal path length corresponds
1894 to the free schedule.
1895 Note, however, that C<isl_map_lexmax> expects the maximum to be
1896 finite, so if the path lengths are unbounded (possibly due to
1897 the overapproximation), then you will get an error message.
1901 __isl_give isl_basic_set *isl_basic_map_wrap(
1902 __isl_take isl_basic_map *bmap);
1903 __isl_give isl_set *isl_map_wrap(
1904 __isl_take isl_map *map);
1905 __isl_give isl_union_set *isl_union_map_wrap(
1906 __isl_take isl_union_map *umap);
1907 __isl_give isl_basic_map *isl_basic_set_unwrap(
1908 __isl_take isl_basic_set *bset);
1909 __isl_give isl_map *isl_set_unwrap(
1910 __isl_take isl_set *set);
1911 __isl_give isl_union_map *isl_union_set_unwrap(
1912 __isl_take isl_union_set *uset);
1916 Remove any internal structure of domain (and range) of the given
1917 set or relation. If there is any such internal structure in the input,
1918 then the name of the space is also removed.
1920 __isl_give isl_basic_set *isl_basic_set_flatten(
1921 __isl_take isl_basic_set *bset);
1922 __isl_give isl_set *isl_set_flatten(
1923 __isl_take isl_set *set);
1924 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1925 __isl_take isl_basic_map *bmap);
1926 __isl_give isl_map *isl_map_flatten_range(
1927 __isl_take isl_map *map);
1928 __isl_give isl_basic_map *isl_basic_map_flatten(
1929 __isl_take isl_basic_map *bmap);
1930 __isl_give isl_map *isl_map_flatten(
1931 __isl_take isl_map *map);
1933 __isl_give isl_map *isl_set_flatten_map(
1934 __isl_take isl_set *set);
1936 The function above constructs a relation
1937 that maps the input set to a flattened version of the set.
1941 Lift the input set to a space with extra dimensions corresponding
1942 to the existentially quantified variables in the input.
1943 In particular, the result lives in a wrapped map where the domain
1944 is the original space and the range corresponds to the original
1945 existentially quantified variables.
1947 __isl_give isl_basic_set *isl_basic_set_lift(
1948 __isl_take isl_basic_set *bset);
1949 __isl_give isl_set *isl_set_lift(
1950 __isl_take isl_set *set);
1951 __isl_give isl_union_set *isl_union_set_lift(
1952 __isl_take isl_union_set *uset);
1954 =item * Internal Product
1956 __isl_give isl_basic_map *isl_basic_map_zip(
1957 __isl_take isl_basic_map *bmap);
1958 __isl_give isl_map *isl_map_zip(
1959 __isl_take isl_map *map);
1960 __isl_give isl_union_map *isl_union_map_zip(
1961 __isl_take isl_union_map *umap);
1963 Given a relation with nested relations for domain and range,
1964 interchange the range of the domain with the domain of the range.
1966 =item * Aligning parameters
1968 __isl_give isl_set *isl_set_align_params(
1969 __isl_take isl_set *set,
1970 __isl_take isl_dim *model);
1971 __isl_give isl_map *isl_map_align_params(
1972 __isl_take isl_map *map,
1973 __isl_take isl_dim *model);
1975 Change the order of the parameters of the given set or relation
1976 such that the first parameters match those of C<model>.
1977 This may involve the introduction of extra parameters.
1978 All parameters need to be named.
1980 =item * Dimension manipulation
1982 __isl_give isl_set *isl_set_add_dims(
1983 __isl_take isl_set *set,
1984 enum isl_dim_type type, unsigned n);
1985 __isl_give isl_map *isl_map_add_dims(
1986 __isl_take isl_map *map,
1987 enum isl_dim_type type, unsigned n);
1988 __isl_give isl_set *isl_set_insert_dims(
1989 __isl_take isl_set *set,
1990 enum isl_dim_type type, unsigned pos, unsigned n);
1991 __isl_give isl_map *isl_map_insert_dims(
1992 __isl_take isl_map *map,
1993 enum isl_dim_type type, unsigned pos, unsigned n);
1995 It is usually not advisable to directly change the (input or output)
1996 space of a set or a relation as this removes the name and the internal
1997 structure of the space. However, the above functions can be useful
1998 to add new parameters, assuming
1999 C<isl_set_align_params> and C<isl_map_align_params>
2004 =head2 Binary Operations
2006 The two arguments of a binary operation not only need to live
2007 in the same C<isl_ctx>, they currently also need to have
2008 the same (number of) parameters.
2010 =head3 Basic Operations
2014 =item * Intersection
2016 __isl_give isl_basic_set *isl_basic_set_intersect(
2017 __isl_take isl_basic_set *bset1,
2018 __isl_take isl_basic_set *bset2);
2019 __isl_give isl_set *isl_set_intersect_params(
2020 __isl_take isl_set *set,
2021 __isl_take isl_set *params);
2022 __isl_give isl_set *isl_set_intersect(
2023 __isl_take isl_set *set1,
2024 __isl_take isl_set *set2);
2025 __isl_give isl_union_set *isl_union_set_intersect(
2026 __isl_take isl_union_set *uset1,
2027 __isl_take isl_union_set *uset2);
2028 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2029 __isl_take isl_basic_map *bmap,
2030 __isl_take isl_basic_set *bset);
2031 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2032 __isl_take isl_basic_map *bmap,
2033 __isl_take isl_basic_set *bset);
2034 __isl_give isl_basic_map *isl_basic_map_intersect(
2035 __isl_take isl_basic_map *bmap1,
2036 __isl_take isl_basic_map *bmap2);
2037 __isl_give isl_map *isl_map_intersect_params(
2038 __isl_take isl_map *map,
2039 __isl_take isl_set *params);
2040 __isl_give isl_map *isl_map_intersect_domain(
2041 __isl_take isl_map *map,
2042 __isl_take isl_set *set);
2043 __isl_give isl_map *isl_map_intersect_range(
2044 __isl_take isl_map *map,
2045 __isl_take isl_set *set);
2046 __isl_give isl_map *isl_map_intersect(
2047 __isl_take isl_map *map1,
2048 __isl_take isl_map *map2);
2049 __isl_give isl_union_map *isl_union_map_intersect_domain(
2050 __isl_take isl_union_map *umap,
2051 __isl_take isl_union_set *uset);
2052 __isl_give isl_union_map *isl_union_map_intersect_range(
2053 __isl_take isl_union_map *umap,
2054 __isl_take isl_union_set *uset);
2055 __isl_give isl_union_map *isl_union_map_intersect(
2056 __isl_take isl_union_map *umap1,
2057 __isl_take isl_union_map *umap2);
2061 __isl_give isl_set *isl_basic_set_union(
2062 __isl_take isl_basic_set *bset1,
2063 __isl_take isl_basic_set *bset2);
2064 __isl_give isl_map *isl_basic_map_union(
2065 __isl_take isl_basic_map *bmap1,
2066 __isl_take isl_basic_map *bmap2);
2067 __isl_give isl_set *isl_set_union(
2068 __isl_take isl_set *set1,
2069 __isl_take isl_set *set2);
2070 __isl_give isl_map *isl_map_union(
2071 __isl_take isl_map *map1,
2072 __isl_take isl_map *map2);
2073 __isl_give isl_union_set *isl_union_set_union(
2074 __isl_take isl_union_set *uset1,
2075 __isl_take isl_union_set *uset2);
2076 __isl_give isl_union_map *isl_union_map_union(
2077 __isl_take isl_union_map *umap1,
2078 __isl_take isl_union_map *umap2);
2080 =item * Set difference
2082 __isl_give isl_set *isl_set_subtract(
2083 __isl_take isl_set *set1,
2084 __isl_take isl_set *set2);
2085 __isl_give isl_map *isl_map_subtract(
2086 __isl_take isl_map *map1,
2087 __isl_take isl_map *map2);
2088 __isl_give isl_union_set *isl_union_set_subtract(
2089 __isl_take isl_union_set *uset1,
2090 __isl_take isl_union_set *uset2);
2091 __isl_give isl_union_map *isl_union_map_subtract(
2092 __isl_take isl_union_map *umap1,
2093 __isl_take isl_union_map *umap2);
2097 __isl_give isl_basic_set *isl_basic_set_apply(
2098 __isl_take isl_basic_set *bset,
2099 __isl_take isl_basic_map *bmap);
2100 __isl_give isl_set *isl_set_apply(
2101 __isl_take isl_set *set,
2102 __isl_take isl_map *map);
2103 __isl_give isl_union_set *isl_union_set_apply(
2104 __isl_take isl_union_set *uset,
2105 __isl_take isl_union_map *umap);
2106 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2107 __isl_take isl_basic_map *bmap1,
2108 __isl_take isl_basic_map *bmap2);
2109 __isl_give isl_basic_map *isl_basic_map_apply_range(
2110 __isl_take isl_basic_map *bmap1,
2111 __isl_take isl_basic_map *bmap2);
2112 __isl_give isl_map *isl_map_apply_domain(
2113 __isl_take isl_map *map1,
2114 __isl_take isl_map *map2);
2115 __isl_give isl_union_map *isl_union_map_apply_domain(
2116 __isl_take isl_union_map *umap1,
2117 __isl_take isl_union_map *umap2);
2118 __isl_give isl_map *isl_map_apply_range(
2119 __isl_take isl_map *map1,
2120 __isl_take isl_map *map2);
2121 __isl_give isl_union_map *isl_union_map_apply_range(
2122 __isl_take isl_union_map *umap1,
2123 __isl_take isl_union_map *umap2);
2125 =item * Cartesian Product
2127 __isl_give isl_set *isl_set_product(
2128 __isl_take isl_set *set1,
2129 __isl_take isl_set *set2);
2130 __isl_give isl_union_set *isl_union_set_product(
2131 __isl_take isl_union_set *uset1,
2132 __isl_take isl_union_set *uset2);
2133 __isl_give isl_basic_map *isl_basic_map_range_product(
2134 __isl_take isl_basic_map *bmap1,
2135 __isl_take isl_basic_map *bmap2);
2136 __isl_give isl_map *isl_map_range_product(
2137 __isl_take isl_map *map1,
2138 __isl_take isl_map *map2);
2139 __isl_give isl_union_map *isl_union_map_range_product(
2140 __isl_take isl_union_map *umap1,
2141 __isl_take isl_union_map *umap2);
2142 __isl_give isl_map *isl_map_product(
2143 __isl_take isl_map *map1,
2144 __isl_take isl_map *map2);
2145 __isl_give isl_union_map *isl_union_map_product(
2146 __isl_take isl_union_map *umap1,
2147 __isl_take isl_union_map *umap2);
2149 The above functions compute the cross product of the given
2150 sets or relations. The domains and ranges of the results
2151 are wrapped maps between domains and ranges of the inputs.
2152 To obtain a ``flat'' product, use the following functions
2155 __isl_give isl_basic_set *isl_basic_set_flat_product(
2156 __isl_take isl_basic_set *bset1,
2157 __isl_take isl_basic_set *bset2);
2158 __isl_give isl_set *isl_set_flat_product(
2159 __isl_take isl_set *set1,
2160 __isl_take isl_set *set2);
2161 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2162 __isl_take isl_basic_map *bmap1,
2163 __isl_take isl_basic_map *bmap2);
2164 __isl_give isl_map *isl_map_flat_range_product(
2165 __isl_take isl_map *map1,
2166 __isl_take isl_map *map2);
2167 __isl_give isl_union_map *isl_union_map_flat_range_product(
2168 __isl_take isl_union_map *umap1,
2169 __isl_take isl_union_map *umap2);
2170 __isl_give isl_basic_map *isl_basic_map_flat_product(
2171 __isl_take isl_basic_map *bmap1,
2172 __isl_take isl_basic_map *bmap2);
2173 __isl_give isl_map *isl_map_flat_product(
2174 __isl_take isl_map *map1,
2175 __isl_take isl_map *map2);
2177 =item * Simplification
2179 __isl_give isl_basic_set *isl_basic_set_gist(
2180 __isl_take isl_basic_set *bset,
2181 __isl_take isl_basic_set *context);
2182 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2183 __isl_take isl_set *context);
2184 __isl_give isl_union_set *isl_union_set_gist(
2185 __isl_take isl_union_set *uset,
2186 __isl_take isl_union_set *context);
2187 __isl_give isl_basic_map *isl_basic_map_gist(
2188 __isl_take isl_basic_map *bmap,
2189 __isl_take isl_basic_map *context);
2190 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2191 __isl_take isl_map *context);
2192 __isl_give isl_union_map *isl_union_map_gist(
2193 __isl_take isl_union_map *umap,
2194 __isl_take isl_union_map *context);
2196 The gist operation returns a set or relation that has the
2197 same intersection with the context as the input set or relation.
2198 Any implicit equality in the intersection is made explicit in the result,
2199 while all inequalities that are redundant with respect to the intersection
2201 In case of union sets and relations, the gist operation is performed
2206 =head3 Lexicographic Optimization
2208 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2209 the following functions
2210 compute a set that contains the lexicographic minimum or maximum
2211 of the elements in C<set> (or C<bset>) for those values of the parameters
2212 that satisfy C<dom>.
2213 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2214 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2216 In other words, the union of the parameter values
2217 for which the result is non-empty and of C<*empty>
2220 __isl_give isl_set *isl_basic_set_partial_lexmin(
2221 __isl_take isl_basic_set *bset,
2222 __isl_take isl_basic_set *dom,
2223 __isl_give isl_set **empty);
2224 __isl_give isl_set *isl_basic_set_partial_lexmax(
2225 __isl_take isl_basic_set *bset,
2226 __isl_take isl_basic_set *dom,
2227 __isl_give isl_set **empty);
2228 __isl_give isl_set *isl_set_partial_lexmin(
2229 __isl_take isl_set *set, __isl_take isl_set *dom,
2230 __isl_give isl_set **empty);
2231 __isl_give isl_set *isl_set_partial_lexmax(
2232 __isl_take isl_set *set, __isl_take isl_set *dom,
2233 __isl_give isl_set **empty);
2235 Given a (basic) set C<set> (or C<bset>), the following functions simply
2236 return a set containing the lexicographic minimum or maximum
2237 of the elements in C<set> (or C<bset>).
2238 In case of union sets, the optimum is computed per space.
2240 __isl_give isl_set *isl_basic_set_lexmin(
2241 __isl_take isl_basic_set *bset);
2242 __isl_give isl_set *isl_basic_set_lexmax(
2243 __isl_take isl_basic_set *bset);
2244 __isl_give isl_set *isl_set_lexmin(
2245 __isl_take isl_set *set);
2246 __isl_give isl_set *isl_set_lexmax(
2247 __isl_take isl_set *set);
2248 __isl_give isl_union_set *isl_union_set_lexmin(
2249 __isl_take isl_union_set *uset);
2250 __isl_give isl_union_set *isl_union_set_lexmax(
2251 __isl_take isl_union_set *uset);
2253 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2254 the following functions
2255 compute a relation that maps each element of C<dom>
2256 to the single lexicographic minimum or maximum
2257 of the elements that are associated to that same
2258 element in C<map> (or C<bmap>).
2259 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2260 that contains the elements in C<dom> that do not map
2261 to any elements in C<map> (or C<bmap>).
2262 In other words, the union of the domain of the result and of C<*empty>
2265 __isl_give isl_map *isl_basic_map_partial_lexmax(
2266 __isl_take isl_basic_map *bmap,
2267 __isl_take isl_basic_set *dom,
2268 __isl_give isl_set **empty);
2269 __isl_give isl_map *isl_basic_map_partial_lexmin(
2270 __isl_take isl_basic_map *bmap,
2271 __isl_take isl_basic_set *dom,
2272 __isl_give isl_set **empty);
2273 __isl_give isl_map *isl_map_partial_lexmax(
2274 __isl_take isl_map *map, __isl_take isl_set *dom,
2275 __isl_give isl_set **empty);
2276 __isl_give isl_map *isl_map_partial_lexmin(
2277 __isl_take isl_map *map, __isl_take isl_set *dom,
2278 __isl_give isl_set **empty);
2280 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2281 return a map mapping each element in the domain of
2282 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2283 of all elements associated to that element.
2284 In case of union relations, the optimum is computed per space.
2286 __isl_give isl_map *isl_basic_map_lexmin(
2287 __isl_take isl_basic_map *bmap);
2288 __isl_give isl_map *isl_basic_map_lexmax(
2289 __isl_take isl_basic_map *bmap);
2290 __isl_give isl_map *isl_map_lexmin(
2291 __isl_take isl_map *map);
2292 __isl_give isl_map *isl_map_lexmax(
2293 __isl_take isl_map *map);
2294 __isl_give isl_union_map *isl_union_map_lexmin(
2295 __isl_take isl_union_map *umap);
2296 __isl_give isl_union_map *isl_union_map_lexmax(
2297 __isl_take isl_union_map *umap);
2301 Lists are defined over several element types, including
2302 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2303 Here we take lists of C<isl_set>s as an example.
2304 Lists can be created, copied and freed using the following functions.
2306 #include <isl/list.h>
2307 __isl_give isl_set_list *isl_set_list_from_set(
2308 __isl_take isl_set *el);
2309 __isl_give isl_set_list *isl_set_list_alloc(
2310 isl_ctx *ctx, int n);
2311 __isl_give isl_set_list *isl_set_list_copy(
2312 __isl_keep isl_set_list *list);
2313 __isl_give isl_set_list *isl_set_list_add(
2314 __isl_take isl_set_list *list,
2315 __isl_take isl_set *el);
2316 __isl_give isl_set_list *isl_set_list_concat(
2317 __isl_take isl_set_list *list1,
2318 __isl_take isl_set_list *list2);
2319 void *isl_set_list_free(__isl_take isl_set_list *list);
2321 C<isl_set_list_alloc> creates an empty list with a capacity for
2322 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2325 Lists can be inspected using the following functions.
2327 #include <isl/list.h>
2328 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2329 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2330 __isl_give isl_set *isl_set_list_get_set(
2331 __isl_keep isl_set_list *list, int index);
2332 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2333 int (*fn)(__isl_take isl_set *el, void *user),
2336 Lists can be printed using
2338 #include <isl/list.h>
2339 __isl_give isl_printer *isl_printer_print_set_list(
2340 __isl_take isl_printer *p,
2341 __isl_keep isl_set_list *list);
2345 Matrices can be created, copied and freed using the following functions.
2347 #include <isl/mat.h>
2348 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2349 unsigned n_row, unsigned n_col);
2350 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2351 void isl_mat_free(__isl_take isl_mat *mat);
2353 Note that the elements of a newly created matrix may have arbitrary values.
2354 The elements can be changed and inspected using the following functions.
2356 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2357 int isl_mat_rows(__isl_keep isl_mat *mat);
2358 int isl_mat_cols(__isl_keep isl_mat *mat);
2359 int isl_mat_get_element(__isl_keep isl_mat *mat,
2360 int row, int col, isl_int *v);
2361 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2362 int row, int col, isl_int v);
2363 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2364 int row, int col, int v);
2366 C<isl_mat_get_element> will return a negative value if anything went wrong.
2367 In that case, the value of C<*v> is undefined.
2369 The following function can be used to compute the (right) inverse
2370 of a matrix, i.e., a matrix such that the product of the original
2371 and the inverse (in that order) is a multiple of the identity matrix.
2372 The input matrix is assumed to be of full row-rank.
2374 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2376 The following function can be used to compute the (right) kernel
2377 (or null space) of a matrix, i.e., a matrix such that the product of
2378 the original and the kernel (in that order) is the zero matrix.
2380 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2382 =head2 Piecewise Quasi Affine Expressions
2384 The zero quasi affine expression can be created using
2386 __isl_give isl_aff *isl_aff_zero(
2387 __isl_take isl_local_space *ls);
2389 A quasi affine expression can also be initialized from an C<isl_div>:
2391 #include <isl/div.h>
2392 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2394 An empty piecewise quasi affine expression (one with no cells)
2395 or a piecewise quasi affine expression with a single cell can
2396 be created using the following functions.
2398 #include <isl/aff.h>
2399 __isl_give isl_pw_aff *isl_pw_aff_empty(
2400 __isl_take isl_dim *dim);
2401 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2402 __isl_take isl_set *set, __isl_take isl_aff *aff);
2403 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2404 __isl_take isl_aff *aff);
2406 Quasi affine expressions can be copied and freed using
2408 #include <isl/aff.h>
2409 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2410 void *isl_aff_free(__isl_take isl_aff *aff);
2412 __isl_give isl_pw_aff *isl_pw_aff_copy(
2413 __isl_keep isl_pw_aff *pwaff);
2414 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2416 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2417 using the following function. The constraint is required to have
2418 a non-zero coefficient for the specified dimension.
2420 #include <isl/constraint.h>
2421 __isl_give isl_aff *isl_constraint_get_bound(
2422 __isl_keep isl_constraint *constraint,
2423 enum isl_dim_type type, int pos);
2425 The entire affine expression of the constraint can also be extracted
2426 using the following function.
2428 #include <isl/constraint.h>
2429 __isl_give isl_aff *isl_constraint_get_aff(
2430 __isl_keep isl_constraint *constraint);
2432 Conversely, an equality constraint equating
2433 the affine expression to zero or an inequality constraint enforcing
2434 the affine expression to be non-negative, can be constructed using
2436 __isl_give isl_constraint *isl_equality_from_aff(
2437 __isl_take isl_aff *aff);
2438 __isl_give isl_constraint *isl_inequality_from_aff(
2439 __isl_take isl_aff *aff);
2441 The expression can be inspected using
2443 #include <isl/aff.h>
2444 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2445 int isl_aff_dim(__isl_keep isl_aff *aff,
2446 enum isl_dim_type type);
2447 __isl_give isl_local_space *isl_aff_get_local_space(
2448 __isl_keep isl_aff *aff);
2449 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2450 enum isl_dim_type type, unsigned pos);
2451 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2453 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2454 enum isl_dim_type type, int pos, isl_int *v);
2455 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2457 __isl_give isl_div *isl_aff_get_div(
2458 __isl_keep isl_aff *aff, int pos);
2460 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2461 int (*fn)(__isl_take isl_set *set,
2462 __isl_take isl_aff *aff,
2463 void *user), void *user);
2465 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2466 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2468 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2469 enum isl_dim_type type, unsigned first, unsigned n);
2470 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2471 enum isl_dim_type type, unsigned first, unsigned n);
2473 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2474 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2475 enum isl_dim_type type);
2476 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2478 It can be modified using
2480 #include <isl/aff.h>
2481 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2482 __isl_take isl_pw_aff *pwaff,
2483 __isl_take isl_id *id);
2484 __isl_give isl_aff *isl_aff_set_dim_name(
2485 __isl_take isl_aff *aff, enum isl_dim_type type,
2486 unsigned pos, const char *s);
2487 __isl_give isl_aff *isl_aff_set_constant(
2488 __isl_take isl_aff *aff, isl_int v);
2489 __isl_give isl_aff *isl_aff_set_constant_si(
2490 __isl_take isl_aff *aff, int v);
2491 __isl_give isl_aff *isl_aff_set_coefficient(
2492 __isl_take isl_aff *aff,
2493 enum isl_dim_type type, int pos, isl_int v);
2494 __isl_give isl_aff *isl_aff_set_coefficient_si(
2495 __isl_take isl_aff *aff,
2496 enum isl_dim_type type, int pos, int v);
2497 __isl_give isl_aff *isl_aff_set_denominator(
2498 __isl_take isl_aff *aff, isl_int v);
2500 __isl_give isl_aff *isl_aff_add_constant(
2501 __isl_take isl_aff *aff, isl_int v);
2502 __isl_give isl_aff *isl_aff_add_constant_si(
2503 __isl_take isl_aff *aff, int v);
2504 __isl_give isl_aff *isl_aff_add_coefficient(
2505 __isl_take isl_aff *aff,
2506 enum isl_dim_type type, int pos, isl_int v);
2507 __isl_give isl_aff *isl_aff_add_coefficient_si(
2508 __isl_take isl_aff *aff,
2509 enum isl_dim_type type, int pos, int v);
2511 __isl_give isl_aff *isl_aff_insert_dims(
2512 __isl_take isl_aff *aff,
2513 enum isl_dim_type type, unsigned first, unsigned n);
2514 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2515 __isl_take isl_pw_aff *pwaff,
2516 enum isl_dim_type type, unsigned first, unsigned n);
2517 __isl_give isl_aff *isl_aff_add_dims(
2518 __isl_take isl_aff *aff,
2519 enum isl_dim_type type, unsigned n);
2520 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2521 __isl_take isl_pw_aff *pwaff,
2522 enum isl_dim_type type, unsigned n);
2523 __isl_give isl_aff *isl_aff_drop_dims(
2524 __isl_take isl_aff *aff,
2525 enum isl_dim_type type, unsigned first, unsigned n);
2526 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2527 __isl_take isl_pw_aff *pwaff,
2528 enum isl_dim_type type, unsigned first, unsigned n);
2530 Note that the C<set_constant> and C<set_coefficient> functions
2531 set the I<numerator> of the constant or coefficient, while
2532 C<add_constant> and C<add_coefficient> add an integer value to
2533 the possibly rational constant or coefficient.
2535 To check whether an affine expressions is obviously zero
2536 or obviously equal to some other affine expression, use
2538 #include <isl/aff.h>
2539 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2540 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2541 __isl_keep isl_aff *aff2);
2545 #include <isl/aff.h>
2546 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2547 __isl_take isl_aff *aff2);
2548 __isl_give isl_pw_aff *isl_pw_aff_add(
2549 __isl_take isl_pw_aff *pwaff1,
2550 __isl_take isl_pw_aff *pwaff2);
2551 __isl_give isl_pw_aff *isl_pw_aff_min(
2552 __isl_take isl_pw_aff *pwaff1,
2553 __isl_take isl_pw_aff *pwaff2);
2554 __isl_give isl_pw_aff *isl_pw_aff_max(
2555 __isl_take isl_pw_aff *pwaff1,
2556 __isl_take isl_pw_aff *pwaff2);
2557 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2558 __isl_take isl_aff *aff2);
2559 __isl_give isl_pw_aff *isl_pw_aff_sub(
2560 __isl_take isl_pw_aff *pwaff1,
2561 __isl_take isl_pw_aff *pwaff2);
2562 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2563 __isl_give isl_pw_aff *isl_pw_aff_neg(
2564 __isl_take isl_pw_aff *pwaff);
2565 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2566 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2567 __isl_take isl_pw_aff *pwaff);
2568 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2569 __isl_give isl_pw_aff *isl_pw_aff_floor(
2570 __isl_take isl_pw_aff *pwaff);
2571 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2573 __isl_give isl_pw_aff *isl_pw_aff_mod(
2574 __isl_take isl_pw_aff *pwaff, isl_int mod);
2575 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2577 __isl_give isl_pw_aff *isl_pw_aff_scale(
2578 __isl_take isl_pw_aff *pwaff, isl_int f);
2579 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2581 __isl_give isl_aff *isl_aff_scale_down_ui(
2582 __isl_take isl_aff *aff, unsigned f);
2583 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2584 __isl_take isl_pw_aff *pwaff, isl_int f);
2586 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2587 __isl_take isl_pw_aff_list *list);
2588 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2589 __isl_take isl_pw_aff_list *list);
2591 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2592 __isl_take isl_pw_aff *pwqp);
2594 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2595 __isl_take isl_pw_aff *pwaff,
2596 __isl_take isl_dim *model);
2598 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2599 __isl_take isl_set *context);
2600 __isl_give isl_pw_aff *isl_pw_aff_gist(
2601 __isl_take isl_pw_aff *pwaff,
2602 __isl_take isl_set *context);
2604 __isl_give isl_set *isl_pw_aff_domain(
2605 __isl_take isl_pw_aff *pwaff);
2607 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2608 __isl_take isl_aff *aff2);
2609 __isl_give isl_pw_aff *isl_pw_aff_mul(
2610 __isl_take isl_pw_aff *pwaff1,
2611 __isl_take isl_pw_aff *pwaff2);
2613 When multiplying two affine expressions, at least one of the two needs
2616 #include <isl/aff.h>
2617 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2618 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2619 __isl_give isl_set *isl_pw_aff_eq_set(
2620 __isl_take isl_pw_aff *pwaff1,
2621 __isl_take isl_pw_aff *pwaff2);
2622 __isl_give isl_set *isl_pw_aff_ne_set(
2623 __isl_take isl_pw_aff *pwaff1,
2624 __isl_take isl_pw_aff *pwaff2);
2625 __isl_give isl_set *isl_pw_aff_le_set(
2626 __isl_take isl_pw_aff *pwaff1,
2627 __isl_take isl_pw_aff *pwaff2);
2628 __isl_give isl_set *isl_pw_aff_lt_set(
2629 __isl_take isl_pw_aff *pwaff1,
2630 __isl_take isl_pw_aff *pwaff2);
2631 __isl_give isl_set *isl_pw_aff_ge_set(
2632 __isl_take isl_pw_aff *pwaff1,
2633 __isl_take isl_pw_aff *pwaff2);
2634 __isl_give isl_set *isl_pw_aff_gt_set(
2635 __isl_take isl_pw_aff *pwaff1,
2636 __isl_take isl_pw_aff *pwaff2);
2638 __isl_give isl_set *isl_pw_aff_list_eq_set(
2639 __isl_take isl_pw_aff_list *list1,
2640 __isl_take isl_pw_aff_list *list2);
2641 __isl_give isl_set *isl_pw_aff_list_ne_set(
2642 __isl_take isl_pw_aff_list *list1,
2643 __isl_take isl_pw_aff_list *list2);
2644 __isl_give isl_set *isl_pw_aff_list_le_set(
2645 __isl_take isl_pw_aff_list *list1,
2646 __isl_take isl_pw_aff_list *list2);
2647 __isl_give isl_set *isl_pw_aff_list_lt_set(
2648 __isl_take isl_pw_aff_list *list1,
2649 __isl_take isl_pw_aff_list *list2);
2650 __isl_give isl_set *isl_pw_aff_list_ge_set(
2651 __isl_take isl_pw_aff_list *list1,
2652 __isl_take isl_pw_aff_list *list2);
2653 __isl_give isl_set *isl_pw_aff_list_gt_set(
2654 __isl_take isl_pw_aff_list *list1,
2655 __isl_take isl_pw_aff_list *list2);
2657 The function C<isl_aff_ge_basic_set> returns a basic set
2658 containing those elements in the shared space
2659 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2660 The function C<isl_aff_ge_set> returns a set
2661 containing those elements in the shared domain
2662 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2663 The functions operating on C<isl_pw_aff_list> apply the corresponding
2664 C<isl_pw_aff> function to each pair of elements in the two lists.
2666 #include <isl/aff.h>
2667 __isl_give isl_set *isl_pw_aff_nonneg_set(
2668 __isl_take isl_pw_aff *pwaff);
2669 __isl_give isl_set *isl_pw_aff_zero_set(
2670 __isl_take isl_pw_aff *pwaff);
2671 __isl_give isl_set *isl_pw_aff_non_zero_set(
2672 __isl_take isl_pw_aff *pwaff);
2674 The function C<isl_pw_aff_nonneg_set> returns a set
2675 containing those elements in the domain
2676 of C<pwaff> where C<pwaff> is non-negative.
2678 #include <isl/aff.h>
2679 __isl_give isl_pw_aff *isl_pw_aff_cond(
2680 __isl_take isl_set *cond,
2681 __isl_take isl_pw_aff *pwaff_true,
2682 __isl_take isl_pw_aff *pwaff_false);
2684 The function C<isl_pw_aff_cond> performs a conditional operator
2685 and returns an expression that is equal to C<pwaff_true>
2686 for elements in C<cond> and equal to C<pwaff_false> for elements
2689 #include <isl/aff.h>
2690 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2691 __isl_take isl_pw_aff *pwaff1,
2692 __isl_take isl_pw_aff *pwaff2);
2694 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2695 expression with a domain that is the union of those of C<pwaff1> and
2696 C<pwaff2> and such that on each cell, the quasi-affine expression is
2697 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2698 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2699 associated expression is the defined one.
2701 An expression can be printed using
2703 #include <isl/aff.h>
2704 __isl_give isl_printer *isl_printer_print_aff(
2705 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2707 __isl_give isl_printer *isl_printer_print_pw_aff(
2708 __isl_take isl_printer *p,
2709 __isl_keep isl_pw_aff *pwaff);
2713 Points are elements of a set. They can be used to construct
2714 simple sets (boxes) or they can be used to represent the
2715 individual elements of a set.
2716 The zero point (the origin) can be created using
2718 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2720 The coordinates of a point can be inspected, set and changed
2723 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2724 enum isl_dim_type type, int pos, isl_int *v);
2725 __isl_give isl_point *isl_point_set_coordinate(
2726 __isl_take isl_point *pnt,
2727 enum isl_dim_type type, int pos, isl_int v);
2729 __isl_give isl_point *isl_point_add_ui(
2730 __isl_take isl_point *pnt,
2731 enum isl_dim_type type, int pos, unsigned val);
2732 __isl_give isl_point *isl_point_sub_ui(
2733 __isl_take isl_point *pnt,
2734 enum isl_dim_type type, int pos, unsigned val);
2736 Other properties can be obtained using
2738 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2740 Points can be copied or freed using
2742 __isl_give isl_point *isl_point_copy(
2743 __isl_keep isl_point *pnt);
2744 void isl_point_free(__isl_take isl_point *pnt);
2746 A singleton set can be created from a point using
2748 __isl_give isl_basic_set *isl_basic_set_from_point(
2749 __isl_take isl_point *pnt);
2750 __isl_give isl_set *isl_set_from_point(
2751 __isl_take isl_point *pnt);
2753 and a box can be created from two opposite extremal points using
2755 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2756 __isl_take isl_point *pnt1,
2757 __isl_take isl_point *pnt2);
2758 __isl_give isl_set *isl_set_box_from_points(
2759 __isl_take isl_point *pnt1,
2760 __isl_take isl_point *pnt2);
2762 All elements of a B<bounded> (union) set can be enumerated using
2763 the following functions.
2765 int isl_set_foreach_point(__isl_keep isl_set *set,
2766 int (*fn)(__isl_take isl_point *pnt, void *user),
2768 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2769 int (*fn)(__isl_take isl_point *pnt, void *user),
2772 The function C<fn> is called for each integer point in
2773 C<set> with as second argument the last argument of
2774 the C<isl_set_foreach_point> call. The function C<fn>
2775 should return C<0> on success and C<-1> on failure.
2776 In the latter case, C<isl_set_foreach_point> will stop
2777 enumerating and return C<-1> as well.
2778 If the enumeration is performed successfully and to completion,
2779 then C<isl_set_foreach_point> returns C<0>.
2781 To obtain a single point of a (basic) set, use
2783 __isl_give isl_point *isl_basic_set_sample_point(
2784 __isl_take isl_basic_set *bset);
2785 __isl_give isl_point *isl_set_sample_point(
2786 __isl_take isl_set *set);
2788 If C<set> does not contain any (integer) points, then the
2789 resulting point will be ``void'', a property that can be
2792 int isl_point_is_void(__isl_keep isl_point *pnt);
2794 =head2 Piecewise Quasipolynomials
2796 A piecewise quasipolynomial is a particular kind of function that maps
2797 a parametric point to a rational value.
2798 More specifically, a quasipolynomial is a polynomial expression in greatest
2799 integer parts of affine expressions of parameters and variables.
2800 A piecewise quasipolynomial is a subdivision of a given parametric
2801 domain into disjoint cells with a quasipolynomial associated to
2802 each cell. The value of the piecewise quasipolynomial at a given
2803 point is the value of the quasipolynomial associated to the cell
2804 that contains the point. Outside of the union of cells,
2805 the value is assumed to be zero.
2806 For example, the piecewise quasipolynomial
2808 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2810 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2811 A given piecewise quasipolynomial has a fixed domain dimension.
2812 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2813 defined over different domains.
2814 Piecewise quasipolynomials are mainly used by the C<barvinok>
2815 library for representing the number of elements in a parametric set or map.
2816 For example, the piecewise quasipolynomial above represents
2817 the number of points in the map
2819 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2821 =head3 Printing (Piecewise) Quasipolynomials
2823 Quasipolynomials and piecewise quasipolynomials can be printed
2824 using the following functions.
2826 __isl_give isl_printer *isl_printer_print_qpolynomial(
2827 __isl_take isl_printer *p,
2828 __isl_keep isl_qpolynomial *qp);
2830 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2831 __isl_take isl_printer *p,
2832 __isl_keep isl_pw_qpolynomial *pwqp);
2834 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2835 __isl_take isl_printer *p,
2836 __isl_keep isl_union_pw_qpolynomial *upwqp);
2838 The output format of the printer
2839 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2840 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2842 In case of printing in C<ISL_FORMAT_C>, the user may want
2843 to set the names of all dimensions
2845 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2846 __isl_take isl_qpolynomial *qp,
2847 enum isl_dim_type type, unsigned pos,
2849 __isl_give isl_pw_qpolynomial *
2850 isl_pw_qpolynomial_set_dim_name(
2851 __isl_take isl_pw_qpolynomial *pwqp,
2852 enum isl_dim_type type, unsigned pos,
2855 =head3 Creating New (Piecewise) Quasipolynomials
2857 Some simple quasipolynomials can be created using the following functions.
2858 More complicated quasipolynomials can be created by applying
2859 operations such as addition and multiplication
2860 on the resulting quasipolynomials
2862 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2863 __isl_take isl_dim *dim);
2864 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2865 __isl_take isl_dim *dim);
2866 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2867 __isl_take isl_dim *dim);
2868 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2869 __isl_take isl_dim *dim);
2870 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2871 __isl_take isl_dim *dim);
2872 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2873 __isl_take isl_dim *dim,
2874 const isl_int n, const isl_int d);
2875 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2876 __isl_take isl_div *div);
2877 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2878 __isl_take isl_dim *dim,
2879 enum isl_dim_type type, unsigned pos);
2880 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2881 __isl_take isl_aff *aff);
2883 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2884 with a single cell can be created using the following functions.
2885 Multiple of these single cell piecewise quasipolynomials can
2886 be combined to create more complicated piecewise quasipolynomials.
2888 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2889 __isl_take isl_dim *dim);
2890 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2891 __isl_take isl_set *set,
2892 __isl_take isl_qpolynomial *qp);
2893 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2894 __isl_take isl_qpolynomial *qp);
2895 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2896 __isl_take isl_pw_aff *pwaff);
2898 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2899 __isl_take isl_dim *dim);
2900 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2901 __isl_take isl_pw_qpolynomial *pwqp);
2902 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2903 __isl_take isl_union_pw_qpolynomial *upwqp,
2904 __isl_take isl_pw_qpolynomial *pwqp);
2906 Quasipolynomials can be copied and freed again using the following
2909 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2910 __isl_keep isl_qpolynomial *qp);
2911 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2913 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2914 __isl_keep isl_pw_qpolynomial *pwqp);
2915 void *isl_pw_qpolynomial_free(
2916 __isl_take isl_pw_qpolynomial *pwqp);
2918 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2919 __isl_keep isl_union_pw_qpolynomial *upwqp);
2920 void isl_union_pw_qpolynomial_free(
2921 __isl_take isl_union_pw_qpolynomial *upwqp);
2923 =head3 Inspecting (Piecewise) Quasipolynomials
2925 To iterate over all piecewise quasipolynomials in a union
2926 piecewise quasipolynomial, use the following function
2928 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2929 __isl_keep isl_union_pw_qpolynomial *upwqp,
2930 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2933 To extract the piecewise quasipolynomial from a union with a given dimension
2936 __isl_give isl_pw_qpolynomial *
2937 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2938 __isl_keep isl_union_pw_qpolynomial *upwqp,
2939 __isl_take isl_dim *dim);
2941 To iterate over the cells in a piecewise quasipolynomial,
2942 use either of the following two functions
2944 int isl_pw_qpolynomial_foreach_piece(
2945 __isl_keep isl_pw_qpolynomial *pwqp,
2946 int (*fn)(__isl_take isl_set *set,
2947 __isl_take isl_qpolynomial *qp,
2948 void *user), void *user);
2949 int isl_pw_qpolynomial_foreach_lifted_piece(
2950 __isl_keep isl_pw_qpolynomial *pwqp,
2951 int (*fn)(__isl_take isl_set *set,
2952 __isl_take isl_qpolynomial *qp,
2953 void *user), void *user);
2955 As usual, the function C<fn> should return C<0> on success
2956 and C<-1> on failure. The difference between
2957 C<isl_pw_qpolynomial_foreach_piece> and
2958 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2959 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2960 compute unique representations for all existentially quantified
2961 variables and then turn these existentially quantified variables
2962 into extra set variables, adapting the associated quasipolynomial
2963 accordingly. This means that the C<set> passed to C<fn>
2964 will not have any existentially quantified variables, but that
2965 the dimensions of the sets may be different for different
2966 invocations of C<fn>.
2968 To iterate over all terms in a quasipolynomial,
2971 int isl_qpolynomial_foreach_term(
2972 __isl_keep isl_qpolynomial *qp,
2973 int (*fn)(__isl_take isl_term *term,
2974 void *user), void *user);
2976 The terms themselves can be inspected and freed using
2979 unsigned isl_term_dim(__isl_keep isl_term *term,
2980 enum isl_dim_type type);
2981 void isl_term_get_num(__isl_keep isl_term *term,
2983 void isl_term_get_den(__isl_keep isl_term *term,
2985 int isl_term_get_exp(__isl_keep isl_term *term,
2986 enum isl_dim_type type, unsigned pos);
2987 __isl_give isl_div *isl_term_get_div(
2988 __isl_keep isl_term *term, unsigned pos);
2989 void isl_term_free(__isl_take isl_term *term);
2991 Each term is a product of parameters, set variables and
2992 integer divisions. The function C<isl_term_get_exp>
2993 returns the exponent of a given dimensions in the given term.
2994 The C<isl_int>s in the arguments of C<isl_term_get_num>
2995 and C<isl_term_get_den> need to have been initialized
2996 using C<isl_int_init> before calling these functions.
2998 =head3 Properties of (Piecewise) Quasipolynomials
3000 To check whether a quasipolynomial is actually a constant,
3001 use the following function.
3003 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3004 isl_int *n, isl_int *d);
3006 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3007 then the numerator and denominator of the constant
3008 are returned in C<*n> and C<*d>, respectively.
3010 =head3 Operations on (Piecewise) Quasipolynomials
3012 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3013 __isl_take isl_qpolynomial *qp, isl_int v);
3014 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3015 __isl_take isl_qpolynomial *qp);
3016 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3017 __isl_take isl_qpolynomial *qp1,
3018 __isl_take isl_qpolynomial *qp2);
3019 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3020 __isl_take isl_qpolynomial *qp1,
3021 __isl_take isl_qpolynomial *qp2);
3022 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3023 __isl_take isl_qpolynomial *qp1,
3024 __isl_take isl_qpolynomial *qp2);
3025 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3026 __isl_take isl_qpolynomial *qp, unsigned exponent);
3028 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3029 __isl_take isl_pw_qpolynomial *pwqp1,
3030 __isl_take isl_pw_qpolynomial *pwqp2);
3031 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3032 __isl_take isl_pw_qpolynomial *pwqp1,
3033 __isl_take isl_pw_qpolynomial *pwqp2);
3034 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3035 __isl_take isl_pw_qpolynomial *pwqp1,
3036 __isl_take isl_pw_qpolynomial *pwqp2);
3037 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3038 __isl_take isl_pw_qpolynomial *pwqp);
3039 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3040 __isl_take isl_pw_qpolynomial *pwqp1,
3041 __isl_take isl_pw_qpolynomial *pwqp2);
3042 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3043 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3045 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3046 __isl_take isl_union_pw_qpolynomial *upwqp1,
3047 __isl_take isl_union_pw_qpolynomial *upwqp2);
3048 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3049 __isl_take isl_union_pw_qpolynomial *upwqp1,
3050 __isl_take isl_union_pw_qpolynomial *upwqp2);
3051 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3052 __isl_take isl_union_pw_qpolynomial *upwqp1,
3053 __isl_take isl_union_pw_qpolynomial *upwqp2);
3055 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3056 __isl_take isl_pw_qpolynomial *pwqp,
3057 __isl_take isl_point *pnt);
3059 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3060 __isl_take isl_union_pw_qpolynomial *upwqp,
3061 __isl_take isl_point *pnt);
3063 __isl_give isl_set *isl_pw_qpolynomial_domain(
3064 __isl_take isl_pw_qpolynomial *pwqp);
3065 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3066 __isl_take isl_pw_qpolynomial *pwpq,
3067 __isl_take isl_set *set);
3069 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3070 __isl_take isl_union_pw_qpolynomial *upwqp);
3071 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3072 __isl_take isl_union_pw_qpolynomial *upwpq,
3073 __isl_take isl_union_set *uset);
3075 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3076 __isl_take isl_qpolynomial *qp,
3077 __isl_take isl_dim *model);
3079 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3080 __isl_take isl_union_pw_qpolynomial *upwqp);
3082 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3083 __isl_take isl_qpolynomial *qp,
3084 __isl_take isl_set *context);
3086 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3087 __isl_take isl_pw_qpolynomial *pwqp,
3088 __isl_take isl_set *context);
3090 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3091 __isl_take isl_union_pw_qpolynomial *upwqp,
3092 __isl_take isl_union_set *context);
3094 The gist operation applies the gist operation to each of
3095 the cells in the domain of the input piecewise quasipolynomial.
3096 The context is also exploited
3097 to simplify the quasipolynomials associated to each cell.
3099 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3100 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3101 __isl_give isl_union_pw_qpolynomial *
3102 isl_union_pw_qpolynomial_to_polynomial(
3103 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3105 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3106 the polynomial will be an overapproximation. If C<sign> is negative,
3107 it will be an underapproximation. If C<sign> is zero, the approximation
3108 will lie somewhere in between.
3110 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3112 A piecewise quasipolynomial reduction is a piecewise
3113 reduction (or fold) of quasipolynomials.
3114 In particular, the reduction can be maximum or a minimum.
3115 The objects are mainly used to represent the result of
3116 an upper or lower bound on a quasipolynomial over its domain,
3117 i.e., as the result of the following function.
3119 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3120 __isl_take isl_pw_qpolynomial *pwqp,
3121 enum isl_fold type, int *tight);
3123 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3124 __isl_take isl_union_pw_qpolynomial *upwqp,
3125 enum isl_fold type, int *tight);
3127 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3128 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3129 is the returned bound is known be tight, i.e., for each value
3130 of the parameters there is at least
3131 one element in the domain that reaches the bound.
3132 If the domain of C<pwqp> is not wrapping, then the bound is computed
3133 over all elements in that domain and the result has a purely parametric
3134 domain. If the domain of C<pwqp> is wrapping, then the bound is
3135 computed over the range of the wrapped relation. The domain of the
3136 wrapped relation becomes the domain of the result.
3138 A (piecewise) quasipolynomial reduction can be copied or freed using the
3139 following functions.
3141 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3142 __isl_keep isl_qpolynomial_fold *fold);
3143 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3144 __isl_keep isl_pw_qpolynomial_fold *pwf);
3145 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3146 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3147 void isl_qpolynomial_fold_free(
3148 __isl_take isl_qpolynomial_fold *fold);
3149 void *isl_pw_qpolynomial_fold_free(
3150 __isl_take isl_pw_qpolynomial_fold *pwf);
3151 void isl_union_pw_qpolynomial_fold_free(
3152 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3154 =head3 Printing Piecewise Quasipolynomial Reductions
3156 Piecewise quasipolynomial reductions can be printed
3157 using the following function.
3159 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3160 __isl_take isl_printer *p,
3161 __isl_keep isl_pw_qpolynomial_fold *pwf);
3162 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3163 __isl_take isl_printer *p,
3164 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3166 For C<isl_printer_print_pw_qpolynomial_fold>,
3167 output format of the printer
3168 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3169 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3170 output format of the printer
3171 needs to be set to C<ISL_FORMAT_ISL>.
3172 In case of printing in C<ISL_FORMAT_C>, the user may want
3173 to set the names of all dimensions
3175 __isl_give isl_pw_qpolynomial_fold *
3176 isl_pw_qpolynomial_fold_set_dim_name(
3177 __isl_take isl_pw_qpolynomial_fold *pwf,
3178 enum isl_dim_type type, unsigned pos,
3181 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3183 To iterate over all piecewise quasipolynomial reductions in a union
3184 piecewise quasipolynomial reduction, use the following function
3186 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3187 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3188 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3189 void *user), void *user);
3191 To iterate over the cells in a piecewise quasipolynomial reduction,
3192 use either of the following two functions
3194 int isl_pw_qpolynomial_fold_foreach_piece(
3195 __isl_keep isl_pw_qpolynomial_fold *pwf,
3196 int (*fn)(__isl_take isl_set *set,
3197 __isl_take isl_qpolynomial_fold *fold,
3198 void *user), void *user);
3199 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3200 __isl_keep isl_pw_qpolynomial_fold *pwf,
3201 int (*fn)(__isl_take isl_set *set,
3202 __isl_take isl_qpolynomial_fold *fold,
3203 void *user), void *user);
3205 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3206 of the difference between these two functions.
3208 To iterate over all quasipolynomials in a reduction, use
3210 int isl_qpolynomial_fold_foreach_qpolynomial(
3211 __isl_keep isl_qpolynomial_fold *fold,
3212 int (*fn)(__isl_take isl_qpolynomial *qp,
3213 void *user), void *user);
3215 =head3 Operations on Piecewise Quasipolynomial Reductions
3217 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3218 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3220 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3221 __isl_take isl_pw_qpolynomial_fold *pwf1,
3222 __isl_take isl_pw_qpolynomial_fold *pwf2);
3224 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3225 __isl_take isl_pw_qpolynomial_fold *pwf1,
3226 __isl_take isl_pw_qpolynomial_fold *pwf2);
3228 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3229 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3230 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3232 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3233 __isl_take isl_pw_qpolynomial_fold *pwf,
3234 __isl_take isl_point *pnt);
3236 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3237 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3238 __isl_take isl_point *pnt);
3240 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3241 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3242 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3243 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3244 __isl_take isl_union_set *uset);
3246 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3247 __isl_take isl_pw_qpolynomial_fold *pwf);
3249 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3250 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3252 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3253 __isl_take isl_pw_qpolynomial_fold *pwf,
3254 __isl_take isl_set *context);
3256 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3257 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3258 __isl_take isl_union_set *context);
3260 The gist operation applies the gist operation to each of
3261 the cells in the domain of the input piecewise quasipolynomial reduction.
3262 In future, the operation will also exploit the context
3263 to simplify the quasipolynomial reductions associated to each cell.
3265 __isl_give isl_pw_qpolynomial_fold *
3266 isl_set_apply_pw_qpolynomial_fold(
3267 __isl_take isl_set *set,
3268 __isl_take isl_pw_qpolynomial_fold *pwf,
3270 __isl_give isl_pw_qpolynomial_fold *
3271 isl_map_apply_pw_qpolynomial_fold(
3272 __isl_take isl_map *map,
3273 __isl_take isl_pw_qpolynomial_fold *pwf,
3275 __isl_give isl_union_pw_qpolynomial_fold *
3276 isl_union_set_apply_union_pw_qpolynomial_fold(
3277 __isl_take isl_union_set *uset,
3278 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3280 __isl_give isl_union_pw_qpolynomial_fold *
3281 isl_union_map_apply_union_pw_qpolynomial_fold(
3282 __isl_take isl_union_map *umap,
3283 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3286 The functions taking a map
3287 compose the given map with the given piecewise quasipolynomial reduction.
3288 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3289 over all elements in the intersection of the range of the map
3290 and the domain of the piecewise quasipolynomial reduction
3291 as a function of an element in the domain of the map.
3292 The functions taking a set compute a bound over all elements in the
3293 intersection of the set and the domain of the
3294 piecewise quasipolynomial reduction.
3296 =head2 Dependence Analysis
3298 C<isl> contains specialized functionality for performing
3299 array dataflow analysis. That is, given a I<sink> access relation
3300 and a collection of possible I<source> access relations,
3301 C<isl> can compute relations that describe
3302 for each iteration of the sink access, which iteration
3303 of which of the source access relations was the last
3304 to access the same data element before the given iteration
3306 To compute standard flow dependences, the sink should be
3307 a read, while the sources should be writes.
3308 If any of the source accesses are marked as being I<may>
3309 accesses, then there will be a dependence to the last
3310 I<must> access B<and> to any I<may> access that follows
3311 this last I<must> access.
3312 In particular, if I<all> sources are I<may> accesses,
3313 then memory based dependence analysis is performed.
3314 If, on the other hand, all sources are I<must> accesses,
3315 then value based dependence analysis is performed.
3317 #include <isl/flow.h>
3319 typedef int (*isl_access_level_before)(void *first, void *second);
3321 __isl_give isl_access_info *isl_access_info_alloc(
3322 __isl_take isl_map *sink,
3323 void *sink_user, isl_access_level_before fn,
3325 __isl_give isl_access_info *isl_access_info_add_source(
3326 __isl_take isl_access_info *acc,
3327 __isl_take isl_map *source, int must,
3329 void isl_access_info_free(__isl_take isl_access_info *acc);
3331 __isl_give isl_flow *isl_access_info_compute_flow(
3332 __isl_take isl_access_info *acc);
3334 int isl_flow_foreach(__isl_keep isl_flow *deps,
3335 int (*fn)(__isl_take isl_map *dep, int must,
3336 void *dep_user, void *user),
3338 __isl_give isl_map *isl_flow_get_no_source(
3339 __isl_keep isl_flow *deps, int must);
3340 void isl_flow_free(__isl_take isl_flow *deps);
3342 The function C<isl_access_info_compute_flow> performs the actual
3343 dependence analysis. The other functions are used to construct
3344 the input for this function or to read off the output.
3346 The input is collected in an C<isl_access_info>, which can
3347 be created through a call to C<isl_access_info_alloc>.
3348 The arguments to this functions are the sink access relation
3349 C<sink>, a token C<sink_user> used to identify the sink
3350 access to the user, a callback function for specifying the
3351 relative order of source and sink accesses, and the number
3352 of source access relations that will be added.
3353 The callback function has type C<int (*)(void *first, void *second)>.
3354 The function is called with two user supplied tokens identifying
3355 either a source or the sink and it should return the shared nesting
3356 level and the relative order of the two accesses.
3357 In particular, let I<n> be the number of loops shared by
3358 the two accesses. If C<first> precedes C<second> textually,
3359 then the function should return I<2 * n + 1>; otherwise,
3360 it should return I<2 * n>.
3361 The sources can be added to the C<isl_access_info> by performing
3362 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3363 C<must> indicates whether the source is a I<must> access
3364 or a I<may> access. Note that a multi-valued access relation
3365 should only be marked I<must> if every iteration in the domain
3366 of the relation accesses I<all> elements in its image.
3367 The C<source_user> token is again used to identify
3368 the source access. The range of the source access relation
3369 C<source> should have the same dimension as the range
3370 of the sink access relation.
3371 The C<isl_access_info_free> function should usually not be
3372 called explicitly, because it is called implicitly by
3373 C<isl_access_info_compute_flow>.
3375 The result of the dependence analysis is collected in an
3376 C<isl_flow>. There may be elements of
3377 the sink access for which no preceding source access could be
3378 found or for which all preceding sources are I<may> accesses.
3379 The relations containing these elements can be obtained through
3380 calls to C<isl_flow_get_no_source>, the first with C<must> set
3381 and the second with C<must> unset.
3382 In the case of standard flow dependence analysis,
3383 with the sink a read and the sources I<must> writes,
3384 the first relation corresponds to the reads from uninitialized
3385 array elements and the second relation is empty.
3386 The actual flow dependences can be extracted using
3387 C<isl_flow_foreach>. This function will call the user-specified
3388 callback function C<fn> for each B<non-empty> dependence between
3389 a source and the sink. The callback function is called
3390 with four arguments, the actual flow dependence relation
3391 mapping source iterations to sink iterations, a boolean that
3392 indicates whether it is a I<must> or I<may> dependence, a token
3393 identifying the source and an additional C<void *> with value
3394 equal to the third argument of the C<isl_flow_foreach> call.
3395 A dependence is marked I<must> if it originates from a I<must>
3396 source and if it is not followed by any I<may> sources.
3398 After finishing with an C<isl_flow>, the user should call
3399 C<isl_flow_free> to free all associated memory.
3401 A higher-level interface to dependence analysis is provided
3402 by the following function.
3404 #include <isl/flow.h>
3406 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3407 __isl_take isl_union_map *must_source,
3408 __isl_take isl_union_map *may_source,
3409 __isl_take isl_union_map *schedule,
3410 __isl_give isl_union_map **must_dep,
3411 __isl_give isl_union_map **may_dep,
3412 __isl_give isl_union_map **must_no_source,
3413 __isl_give isl_union_map **may_no_source);
3415 The arrays are identified by the tuple names of the ranges
3416 of the accesses. The iteration domains by the tuple names
3417 of the domains of the accesses and of the schedule.
3418 The relative order of the iteration domains is given by the
3419 schedule. The relations returned through C<must_no_source>
3420 and C<may_no_source> are subsets of C<sink>.
3421 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3422 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3423 any of the other arguments is treated as an error.
3427 B<The functionality described in this section is fairly new
3428 and may be subject to change.>
3430 The following function can be used to compute a schedule
3431 for a union of domains. The generated schedule respects
3432 all C<validity> dependences. That is, all dependence distances
3433 over these dependences in the scheduled space are lexicographically
3434 positive. The generated schedule schedule also tries to minimize
3435 the dependence distances over C<proximity> dependences.
3436 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3437 for groups of domains where the dependence distances have only
3438 non-negative values.
3439 The algorithm used to construct the schedule is similar to that
3442 #include <isl/schedule.h>
3443 __isl_give isl_schedule *isl_union_set_compute_schedule(
3444 __isl_take isl_union_set *domain,
3445 __isl_take isl_union_map *validity,
3446 __isl_take isl_union_map *proximity);
3447 void *isl_schedule_free(__isl_take isl_schedule *sched);
3449 A mapping from the domains to the scheduled space can be obtained
3450 from an C<isl_schedule> using the following function.
3452 __isl_give isl_union_map *isl_schedule_get_map(
3453 __isl_keep isl_schedule *sched);
3455 A representation of the schedule can be printed using
3457 __isl_give isl_printer *isl_printer_print_schedule(
3458 __isl_take isl_printer *p,
3459 __isl_keep isl_schedule *schedule);
3461 A representation of the schedule as a forest of bands can be obtained
3462 using the following function.
3464 __isl_give isl_band_list *isl_schedule_get_band_forest(
3465 __isl_keep isl_schedule *schedule);
3467 The list can be manipulated as explained in L<"Lists">.
3468 The bands inside the list can be copied and freed using the following
3471 #include <isl/band.h>
3472 __isl_give isl_band *isl_band_copy(
3473 __isl_keep isl_band *band);
3474 void *isl_band_free(__isl_take isl_band *band);
3476 Each band contains zero or more scheduling dimensions.
3477 These are referred to as the members of the band.
3478 The section of the schedule that corresponds to the band is
3479 referred to as the partial schedule of the band.
3480 For those nodes that participate in a band, the outer scheduling
3481 dimensions form the prefix schedule, while the inner scheduling
3482 dimensions form the suffix schedule.
3483 That is, if we take a cut of the band forest, then the union of
3484 the concatenations of the prefix, partial and suffix schedules of
3485 each band in the cut is equal to the entire schedule (modulo
3486 some possible padding at the end with zero scheduling dimensions).
3487 The properties of a band can be inspected using the following functions.
3489 #include <isl/band.h>
3490 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3492 int isl_band_has_children(__isl_keep isl_band *band);
3493 __isl_give isl_band_list *isl_band_get_children(
3494 __isl_keep isl_band *band);
3496 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3497 __isl_keep isl_band *band);
3498 __isl_give isl_union_map *isl_band_get_partial_schedule(
3499 __isl_keep isl_band *band);
3500 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3501 __isl_keep isl_band *band);
3503 int isl_band_n_member(__isl_keep isl_band *band);
3504 int isl_band_member_is_zero_distance(
3505 __isl_keep isl_band *band, int pos);
3507 Note that a scheduling dimension is considered to be ``zero
3508 distance'' if it does not carry any proximity dependences
3510 That is, if the dependence distances of the proximity
3511 dependences are all zero in that direction (for fixed
3512 iterations of outer bands).
3514 A representation of the band can be printed using
3516 #include <isl/band.h>
3517 __isl_give isl_printer *isl_printer_print_band(
3518 __isl_take isl_printer *p,
3519 __isl_keep isl_band *band);
3521 =head2 Parametric Vertex Enumeration
3523 The parametric vertex enumeration described in this section
3524 is mainly intended to be used internally and by the C<barvinok>
3527 #include <isl/vertices.h>
3528 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3529 __isl_keep isl_basic_set *bset);
3531 The function C<isl_basic_set_compute_vertices> performs the
3532 actual computation of the parametric vertices and the chamber
3533 decomposition and store the result in an C<isl_vertices> object.
3534 This information can be queried by either iterating over all
3535 the vertices or iterating over all the chambers or cells
3536 and then iterating over all vertices that are active on the chamber.
3538 int isl_vertices_foreach_vertex(
3539 __isl_keep isl_vertices *vertices,
3540 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3543 int isl_vertices_foreach_cell(
3544 __isl_keep isl_vertices *vertices,
3545 int (*fn)(__isl_take isl_cell *cell, void *user),
3547 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3548 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3551 Other operations that can be performed on an C<isl_vertices> object are
3554 isl_ctx *isl_vertices_get_ctx(
3555 __isl_keep isl_vertices *vertices);
3556 int isl_vertices_get_n_vertices(
3557 __isl_keep isl_vertices *vertices);
3558 void isl_vertices_free(__isl_take isl_vertices *vertices);
3560 Vertices can be inspected and destroyed using the following functions.
3562 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3563 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3564 __isl_give isl_basic_set *isl_vertex_get_domain(
3565 __isl_keep isl_vertex *vertex);
3566 __isl_give isl_basic_set *isl_vertex_get_expr(
3567 __isl_keep isl_vertex *vertex);
3568 void isl_vertex_free(__isl_take isl_vertex *vertex);
3570 C<isl_vertex_get_expr> returns a singleton parametric set describing
3571 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3573 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3574 B<rational> basic sets, so they should mainly be used for inspection
3575 and should not be mixed with integer sets.
3577 Chambers can be inspected and destroyed using the following functions.
3579 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3580 __isl_give isl_basic_set *isl_cell_get_domain(
3581 __isl_keep isl_cell *cell);
3582 void isl_cell_free(__isl_take isl_cell *cell);
3586 Although C<isl> is mainly meant to be used as a library,
3587 it also contains some basic applications that use some
3588 of the functionality of C<isl>.
3589 The input may be specified in either the L<isl format>
3590 or the L<PolyLib format>.
3592 =head2 C<isl_polyhedron_sample>
3594 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3595 an integer element of the polyhedron, if there is any.
3596 The first column in the output is the denominator and is always
3597 equal to 1. If the polyhedron contains no integer points,
3598 then a vector of length zero is printed.
3602 C<isl_pip> takes the same input as the C<example> program
3603 from the C<piplib> distribution, i.e., a set of constraints
3604 on the parameters, a line containing only -1 and finally a set
3605 of constraints on a parametric polyhedron.
3606 The coefficients of the parameters appear in the last columns
3607 (but before the final constant column).
3608 The output is the lexicographic minimum of the parametric polyhedron.
3609 As C<isl> currently does not have its own output format, the output
3610 is just a dump of the internal state.
3612 =head2 C<isl_polyhedron_minimize>
3614 C<isl_polyhedron_minimize> computes the minimum of some linear
3615 or affine objective function over the integer points in a polyhedron.
3616 If an affine objective function
3617 is given, then the constant should appear in the last column.
3619 =head2 C<isl_polytope_scan>
3621 Given a polytope, C<isl_polytope_scan> prints
3622 all integer points in the polytope.