3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
102 =item * The C<isl_dim> type has been renamed to C<isl_space>
103 along with the associated functions.
104 Some of the old names have been kept for backward compatibility,
105 but they will be removed in the future.
111 The source of C<isl> can be obtained either as a tarball
112 or from the git repository. Both are available from
113 L<http://freshmeat.net/projects/isl/>.
114 The installation process depends on how you obtained
117 =head2 Installation from the git repository
121 =item 1 Clone or update the repository
123 The first time the source is obtained, you need to clone
126 git clone git://repo.or.cz/isl.git
128 To obtain updates, you need to pull in the latest changes
132 =item 2 Generate C<configure>
138 After performing the above steps, continue
139 with the L<Common installation instructions>.
141 =head2 Common installation instructions
145 =item 1 Obtain C<GMP>
147 Building C<isl> requires C<GMP>, including its headers files.
148 Your distribution may not provide these header files by default
149 and you may need to install a package called C<gmp-devel> or something
150 similar. Alternatively, C<GMP> can be built from
151 source, available from L<http://gmplib.org/>.
155 C<isl> uses the standard C<autoconf> C<configure> script.
160 optionally followed by some configure options.
161 A complete list of options can be obtained by running
165 Below we discuss some of the more common options.
167 C<isl> can optionally use C<piplib>, but no
168 C<piplib> functionality is currently used by default.
169 The C<--with-piplib> option can
170 be used to specify which C<piplib>
171 library to use, either an installed version (C<system>),
172 an externally built version (C<build>)
173 or no version (C<no>). The option C<build> is mostly useful
174 in C<configure> scripts of larger projects that bundle both C<isl>
181 Installation prefix for C<isl>
183 =item C<--with-gmp-prefix>
185 Installation prefix for C<GMP> (architecture-independent files).
187 =item C<--with-gmp-exec-prefix>
189 Installation prefix for C<GMP> (architecture-dependent files).
191 =item C<--with-piplib>
193 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
195 =item C<--with-piplib-prefix>
197 Installation prefix for C<system> C<piplib> (architecture-independent files).
199 =item C<--with-piplib-exec-prefix>
201 Installation prefix for C<system> C<piplib> (architecture-dependent files).
203 =item C<--with-piplib-builddir>
205 Location where C<build> C<piplib> was built.
213 =item 4 Install (optional)
221 =head2 Initialization
223 All manipulations of integer sets and relations occur within
224 the context of an C<isl_ctx>.
225 A given C<isl_ctx> can only be used within a single thread.
226 All arguments of a function are required to have been allocated
227 within the same context.
228 There are currently no functions available for moving an object
229 from one C<isl_ctx> to another C<isl_ctx>. This means that
230 there is currently no way of safely moving an object from one
231 thread to another, unless the whole C<isl_ctx> is moved.
233 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
234 freed using C<isl_ctx_free>.
235 All objects allocated within an C<isl_ctx> should be freed
236 before the C<isl_ctx> itself is freed.
238 isl_ctx *isl_ctx_alloc();
239 void isl_ctx_free(isl_ctx *ctx);
243 All operations on integers, mainly the coefficients
244 of the constraints describing the sets and relations,
245 are performed in exact integer arithmetic using C<GMP>.
246 However, to allow future versions of C<isl> to optionally
247 support fixed integer arithmetic, all calls to C<GMP>
248 are wrapped inside C<isl> specific macros.
249 The basic type is C<isl_int> and the operations below
250 are available on this type.
251 The meanings of these operations are essentially the same
252 as their C<GMP> C<mpz_> counterparts.
253 As always with C<GMP> types, C<isl_int>s need to be
254 initialized with C<isl_int_init> before they can be used
255 and they need to be released with C<isl_int_clear>
257 The user should not assume that an C<isl_int> is represented
258 as a C<mpz_t>, but should instead explicitly convert between
259 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
260 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
264 =item isl_int_init(i)
266 =item isl_int_clear(i)
268 =item isl_int_set(r,i)
270 =item isl_int_set_si(r,i)
272 =item isl_int_set_gmp(r,g)
274 =item isl_int_get_gmp(i,g)
276 =item isl_int_abs(r,i)
278 =item isl_int_neg(r,i)
280 =item isl_int_swap(i,j)
282 =item isl_int_swap_or_set(i,j)
284 =item isl_int_add_ui(r,i,j)
286 =item isl_int_sub_ui(r,i,j)
288 =item isl_int_add(r,i,j)
290 =item isl_int_sub(r,i,j)
292 =item isl_int_mul(r,i,j)
294 =item isl_int_mul_ui(r,i,j)
296 =item isl_int_addmul(r,i,j)
298 =item isl_int_submul(r,i,j)
300 =item isl_int_gcd(r,i,j)
302 =item isl_int_lcm(r,i,j)
304 =item isl_int_divexact(r,i,j)
306 =item isl_int_cdiv_q(r,i,j)
308 =item isl_int_fdiv_q(r,i,j)
310 =item isl_int_fdiv_r(r,i,j)
312 =item isl_int_fdiv_q_ui(r,i,j)
314 =item isl_int_read(r,s)
316 =item isl_int_print(out,i,width)
320 =item isl_int_cmp(i,j)
322 =item isl_int_cmp_si(i,si)
324 =item isl_int_eq(i,j)
326 =item isl_int_ne(i,j)
328 =item isl_int_lt(i,j)
330 =item isl_int_le(i,j)
332 =item isl_int_gt(i,j)
334 =item isl_int_ge(i,j)
336 =item isl_int_abs_eq(i,j)
338 =item isl_int_abs_ne(i,j)
340 =item isl_int_abs_lt(i,j)
342 =item isl_int_abs_gt(i,j)
344 =item isl_int_abs_ge(i,j)
346 =item isl_int_is_zero(i)
348 =item isl_int_is_one(i)
350 =item isl_int_is_negone(i)
352 =item isl_int_is_pos(i)
354 =item isl_int_is_neg(i)
356 =item isl_int_is_nonpos(i)
358 =item isl_int_is_nonneg(i)
360 =item isl_int_is_divisible_by(i,j)
364 =head2 Sets and Relations
366 C<isl> uses six types of objects for representing sets and relations,
367 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
368 C<isl_union_set> and C<isl_union_map>.
369 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
370 can be described as a conjunction of affine constraints, while
371 C<isl_set> and C<isl_map> represent unions of
372 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
373 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
374 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
375 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
376 where spaces are considered different if they have a different number
377 of dimensions and/or different names (see L<"Spaces">).
378 The difference between sets and relations (maps) is that sets have
379 one set of variables, while relations have two sets of variables,
380 input variables and output variables.
382 =head2 Memory Management
384 Since a high-level operation on sets and/or relations usually involves
385 several substeps and since the user is usually not interested in
386 the intermediate results, most functions that return a new object
387 will also release all the objects passed as arguments.
388 If the user still wants to use one or more of these arguments
389 after the function call, she should pass along a copy of the
390 object rather than the object itself.
391 The user is then responsible for making sure that the original
392 object gets used somewhere else or is explicitly freed.
394 The arguments and return values of all documented functions are
395 annotated to make clear which arguments are released and which
396 arguments are preserved. In particular, the following annotations
403 C<__isl_give> means that a new object is returned.
404 The user should make sure that the returned pointer is
405 used exactly once as a value for an C<__isl_take> argument.
406 In between, it can be used as a value for as many
407 C<__isl_keep> arguments as the user likes.
408 There is one exception, and that is the case where the
409 pointer returned is C<NULL>. Is this case, the user
410 is free to use it as an C<__isl_take> argument or not.
414 C<__isl_take> means that the object the argument points to
415 is taken over by the function and may no longer be used
416 by the user as an argument to any other function.
417 The pointer value must be one returned by a function
418 returning an C<__isl_give> pointer.
419 If the user passes in a C<NULL> value, then this will
420 be treated as an error in the sense that the function will
421 not perform its usual operation. However, it will still
422 make sure that all the other C<__isl_take> arguments
427 C<__isl_keep> means that the function will only use the object
428 temporarily. After the function has finished, the user
429 can still use it as an argument to other functions.
430 A C<NULL> value will be treated in the same way as
431 a C<NULL> value for an C<__isl_take> argument.
437 Identifiers are used to identify both individual dimensions
438 and tuples of dimensions. They consist of a name and an optional
439 pointer. Identifiers with the same name but different pointer values
440 are considered to be distinct.
441 Identifiers can be constructed, copied, freed, inspected and printed
442 using the following functions.
445 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
446 __isl_keep const char *name, void *user);
447 __isl_give isl_id *isl_id_copy(isl_id *id);
448 void *isl_id_free(__isl_take isl_id *id);
450 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
451 void *isl_id_get_user(__isl_keep isl_id *id);
452 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
454 __isl_give isl_printer *isl_printer_print_id(
455 __isl_take isl_printer *p, __isl_keep isl_id *id);
457 Note that C<isl_id_get_name> returns a pointer to some internal
458 data structure, so the result can only be used while the
459 corresponding C<isl_id> is alive.
463 Whenever a new set or relation is created from scratch,
464 the space in which it lives needs to be specified using an C<isl_space>.
466 #include <isl/space.h>
467 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
468 unsigned nparam, unsigned n_in, unsigned n_out);
469 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
470 unsigned nparam, unsigned dim);
471 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
472 void isl_space_free(__isl_take isl_space *space);
473 unsigned isl_space_dim(__isl_keep isl_space *space,
474 enum isl_dim_type type);
476 The space used for creating a set
477 needs to be created using C<isl_space_set_alloc>, while
478 that for creating a relation
479 needs to be created using C<isl_space_alloc>.
480 C<isl_space_dim> can be used
481 to find out the number of dimensions of each type in
482 a space, where type may be
483 C<isl_dim_param>, C<isl_dim_in> (only for relations),
484 C<isl_dim_out> (only for relations), C<isl_dim_set>
485 (only for sets) or C<isl_dim_all>.
487 It is often useful to create objects that live in the
488 same space as some other object. This can be accomplished
489 by creating the new objects
490 (see L<Creating New Sets and Relations> or
491 L<Creating New (Piecewise) Quasipolynomials>) based on the space
492 of the original object.
495 __isl_give isl_space *isl_basic_set_get_space(
496 __isl_keep isl_basic_set *bset);
497 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
499 #include <isl/union_set.h>
500 __isl_give isl_space *isl_union_set_get_space(
501 __isl_keep isl_union_set *uset);
504 __isl_give isl_space *isl_basic_map_get_space(
505 __isl_keep isl_basic_map *bmap);
506 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
508 #include <isl/union_map.h>
509 __isl_give isl_space *isl_union_map_get_space(
510 __isl_keep isl_union_map *umap);
512 #include <isl/constraint.h>
513 __isl_give isl_space *isl_constraint_get_space(
514 __isl_keep isl_constraint *constraint);
516 #include <isl/polynomial.h>
517 __isl_give isl_space *isl_qpolynomial_get_space(
518 __isl_keep isl_qpolynomial *qp);
519 __isl_give isl_space *isl_qpolynomial_fold_get_space(
520 __isl_keep isl_qpolynomial_fold *fold);
521 __isl_give isl_space *isl_pw_qpolynomial_get_space(
522 __isl_keep isl_pw_qpolynomial *pwqp);
523 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
524 __isl_keep isl_union_pw_qpolynomial *upwqp);
525 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
526 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
529 __isl_give isl_space *isl_aff_get_space(
530 __isl_keep isl_aff *aff);
531 __isl_give isl_space *isl_pw_aff_get_space(
532 __isl_keep isl_pw_aff *pwaff);
534 #include <isl/point.h>
535 __isl_give isl_space *isl_point_get_space(
536 __isl_keep isl_point *pnt);
538 The identifiers or names of the individual dimensions may be set or read off
539 using the following functions.
541 #include <isl/space.h>
542 __isl_give isl_space *isl_space_set_dim_id(
543 __isl_take isl_space *space,
544 enum isl_dim_type type, unsigned pos,
545 __isl_take isl_id *id);
546 int isl_space_has_dim_id(__isl_keep isl_space *space,
547 enum isl_dim_type type, unsigned pos);
548 __isl_give isl_id *isl_space_get_dim_id(
549 __isl_keep isl_space *space,
550 enum isl_dim_type type, unsigned pos);
551 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
552 enum isl_dim_type type, unsigned pos,
553 __isl_keep const char *name);
554 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
555 enum isl_dim_type type, unsigned pos);
557 Note that C<isl_space_get_name> returns a pointer to some internal
558 data structure, so the result can only be used while the
559 corresponding C<isl_space> is alive.
560 Also note that every function that operates on two sets or relations
561 requires that both arguments have the same parameters. This also
562 means that if one of the arguments has named parameters, then the
563 other needs to have named parameters too and the names need to match.
564 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
565 arguments may have different parameters (as long as they are named),
566 in which case the result will have as parameters the union of the parameters of
569 Given the identifier of a dimension (typically a parameter),
570 its position can be obtained from the following function.
572 #include <isl/space.h>
573 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
574 enum isl_dim_type type, __isl_keep isl_id *id);
576 The identifiers or names of entire spaces may be set or read off
577 using the following functions.
579 #include <isl/space.h>
580 __isl_give isl_space *isl_space_set_tuple_id(
581 __isl_take isl_space *space,
582 enum isl_dim_type type, __isl_take isl_id *id);
583 __isl_give isl_space *isl_space_reset_tuple_id(
584 __isl_take isl_space *space, enum isl_dim_type type);
585 int isl_space_has_tuple_id(__isl_keep isl_space *space,
586 enum isl_dim_type type);
587 __isl_give isl_id *isl_space_get_tuple_id(
588 __isl_keep isl_space *space, enum isl_dim_type type);
589 __isl_give isl_space *isl_space_set_tuple_name(
590 __isl_take isl_space *space,
591 enum isl_dim_type type, const char *s);
592 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
593 enum isl_dim_type type);
595 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
596 or C<isl_dim_set>. As with C<isl_space_get_name>,
597 the C<isl_space_get_tuple_name> function returns a pointer to some internal
599 Binary operations require the corresponding spaces of their arguments
600 to have the same name.
602 Spaces can be nested. In particular, the domain of a set or
603 the domain or range of a relation can be a nested relation.
604 The following functions can be used to construct and deconstruct
607 #include <isl/space.h>
608 int isl_space_is_wrapping(__isl_keep isl_space *space);
609 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
610 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
612 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
613 be the space of a set, while that of
614 C<isl_space_wrap> should be the space of a relation.
615 Conversely, the output of C<isl_space_unwrap> is the space
616 of a relation, while that of C<isl_space_wrap> is the space of a set.
618 Spaces can be created from other spaces
619 using the following functions.
621 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
622 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
623 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
624 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
625 __isl_give isl_space *isl_space_params(
626 __isl_take isl_space *space);
627 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
628 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
629 __isl_take isl_space *right);
630 __isl_give isl_space *isl_space_align_params(
631 __isl_take isl_space *space1, __isl_take isl_space *space2)
632 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
633 enum isl_dim_type type, unsigned pos, unsigned n);
634 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
635 enum isl_dim_type type, unsigned n);
636 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
637 enum isl_dim_type type, unsigned first, unsigned n);
638 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
639 enum isl_dim_type dst_type, unsigned dst_pos,
640 enum isl_dim_type src_type, unsigned src_pos,
642 __isl_give isl_space *isl_space_map_from_set(
643 __isl_take isl_space *space);
644 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
646 Note that if dimensions are added or removed from a space, then
647 the name and the internal structure are lost.
651 A local space is essentially a space with
652 zero or more existentially quantified variables.
653 The local space of a basic set or relation can be obtained
654 using the following functions.
657 __isl_give isl_local_space *isl_basic_set_get_local_space(
658 __isl_keep isl_basic_set *bset);
661 __isl_give isl_local_space *isl_basic_map_get_local_space(
662 __isl_keep isl_basic_map *bmap);
664 A new local space can be created from a space using
666 #include <isl/local_space.h>
667 __isl_give isl_local_space *isl_local_space_from_space(
668 __isl_take isl_space *space);
670 They can be inspected, copied and freed using the following functions.
672 #include <isl/local_space.h>
673 isl_ctx *isl_local_space_get_ctx(
674 __isl_keep isl_local_space *ls);
675 int isl_local_space_dim(__isl_keep isl_local_space *ls,
676 enum isl_dim_type type);
677 const char *isl_local_space_get_dim_name(
678 __isl_keep isl_local_space *ls,
679 enum isl_dim_type type, unsigned pos);
680 __isl_give isl_local_space *isl_local_space_set_dim_name(
681 __isl_take isl_local_space *ls,
682 enum isl_dim_type type, unsigned pos, const char *s);
683 __isl_give isl_space *isl_local_space_get_space(
684 __isl_keep isl_local_space *ls);
685 __isl_give isl_div *isl_local_space_get_div(
686 __isl_keep isl_local_space *ls, int pos);
687 __isl_give isl_local_space *isl_local_space_copy(
688 __isl_keep isl_local_space *ls);
689 void *isl_local_space_free(__isl_take isl_local_space *ls);
691 Two local spaces can be compared using
693 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
694 __isl_keep isl_local_space *ls2);
696 Local spaces can be created from other local spaces
697 using the following functions.
699 __isl_give isl_local_space *isl_local_space_from_domain(
700 __isl_take isl_local_space *ls);
701 __isl_give isl_local_space *isl_local_space_add_dims(
702 __isl_take isl_local_space *ls,
703 enum isl_dim_type type, unsigned n);
704 __isl_give isl_local_space *isl_local_space_insert_dims(
705 __isl_take isl_local_space *ls,
706 enum isl_dim_type type, unsigned first, unsigned n);
707 __isl_give isl_local_space *isl_local_space_drop_dims(
708 __isl_take isl_local_space *ls,
709 enum isl_dim_type type, unsigned first, unsigned n);
711 =head2 Input and Output
713 C<isl> supports its own input/output format, which is similar
714 to the C<Omega> format, but also supports the C<PolyLib> format
719 The C<isl> format is similar to that of C<Omega>, but has a different
720 syntax for describing the parameters and allows for the definition
721 of an existentially quantified variable as the integer division
722 of an affine expression.
723 For example, the set of integers C<i> between C<0> and C<n>
724 such that C<i % 10 <= 6> can be described as
726 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
729 A set or relation can have several disjuncts, separated
730 by the keyword C<or>. Each disjunct is either a conjunction
731 of constraints or a projection (C<exists>) of a conjunction
732 of constraints. The constraints are separated by the keyword
735 =head3 C<PolyLib> format
737 If the represented set is a union, then the first line
738 contains a single number representing the number of disjuncts.
739 Otherwise, a line containing the number C<1> is optional.
741 Each disjunct is represented by a matrix of constraints.
742 The first line contains two numbers representing
743 the number of rows and columns,
744 where the number of rows is equal to the number of constraints
745 and the number of columns is equal to two plus the number of variables.
746 The following lines contain the actual rows of the constraint matrix.
747 In each row, the first column indicates whether the constraint
748 is an equality (C<0>) or inequality (C<1>). The final column
749 corresponds to the constant term.
751 If the set is parametric, then the coefficients of the parameters
752 appear in the last columns before the constant column.
753 The coefficients of any existentially quantified variables appear
754 between those of the set variables and those of the parameters.
756 =head3 Extended C<PolyLib> format
758 The extended C<PolyLib> format is nearly identical to the
759 C<PolyLib> format. The only difference is that the line
760 containing the number of rows and columns of a constraint matrix
761 also contains four additional numbers:
762 the number of output dimensions, the number of input dimensions,
763 the number of local dimensions (i.e., the number of existentially
764 quantified variables) and the number of parameters.
765 For sets, the number of ``output'' dimensions is equal
766 to the number of set dimensions, while the number of ``input''
772 __isl_give isl_basic_set *isl_basic_set_read_from_file(
773 isl_ctx *ctx, FILE *input, int nparam);
774 __isl_give isl_basic_set *isl_basic_set_read_from_str(
775 isl_ctx *ctx, const char *str, int nparam);
776 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
777 FILE *input, int nparam);
778 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
779 const char *str, int nparam);
782 __isl_give isl_basic_map *isl_basic_map_read_from_file(
783 isl_ctx *ctx, FILE *input, int nparam);
784 __isl_give isl_basic_map *isl_basic_map_read_from_str(
785 isl_ctx *ctx, const char *str, int nparam);
786 __isl_give isl_map *isl_map_read_from_file(
787 isl_ctx *ctx, FILE *input, int nparam);
788 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
789 const char *str, int nparam);
791 #include <isl/union_set.h>
792 __isl_give isl_union_set *isl_union_set_read_from_file(
793 isl_ctx *ctx, FILE *input);
794 __isl_give isl_union_set *isl_union_set_read_from_str(
795 isl_ctx *ctx, const char *str);
797 #include <isl/union_map.h>
798 __isl_give isl_union_map *isl_union_map_read_from_file(
799 isl_ctx *ctx, FILE *input);
800 __isl_give isl_union_map *isl_union_map_read_from_str(
801 isl_ctx *ctx, const char *str);
803 The input format is autodetected and may be either the C<PolyLib> format
804 or the C<isl> format.
805 C<nparam> specifies how many of the final columns in
806 the C<PolyLib> format correspond to parameters.
807 If input is given in the C<isl> format, then the number
808 of parameters needs to be equal to C<nparam>.
809 If C<nparam> is negative, then any number of parameters
810 is accepted in the C<isl> format and zero parameters
811 are assumed in the C<PolyLib> format.
815 Before anything can be printed, an C<isl_printer> needs to
818 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
820 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
821 void isl_printer_free(__isl_take isl_printer *printer);
822 __isl_give char *isl_printer_get_str(
823 __isl_keep isl_printer *printer);
825 The behavior of the printer can be modified in various ways
827 __isl_give isl_printer *isl_printer_set_output_format(
828 __isl_take isl_printer *p, int output_format);
829 __isl_give isl_printer *isl_printer_set_indent(
830 __isl_take isl_printer *p, int indent);
831 __isl_give isl_printer *isl_printer_indent(
832 __isl_take isl_printer *p, int indent);
833 __isl_give isl_printer *isl_printer_set_prefix(
834 __isl_take isl_printer *p, const char *prefix);
835 __isl_give isl_printer *isl_printer_set_suffix(
836 __isl_take isl_printer *p, const char *suffix);
838 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
839 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
840 and defaults to C<ISL_FORMAT_ISL>.
841 Each line in the output is indented by C<indent> (set by
842 C<isl_printer_set_indent>) spaces
843 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
844 In the C<PolyLib> format output,
845 the coefficients of the existentially quantified variables
846 appear between those of the set variables and those
848 The function C<isl_printer_indent> increases the indentation
849 by the specified amount (which may be negative).
851 To actually print something, use
854 __isl_give isl_printer *isl_printer_print_basic_set(
855 __isl_take isl_printer *printer,
856 __isl_keep isl_basic_set *bset);
857 __isl_give isl_printer *isl_printer_print_set(
858 __isl_take isl_printer *printer,
859 __isl_keep isl_set *set);
862 __isl_give isl_printer *isl_printer_print_basic_map(
863 __isl_take isl_printer *printer,
864 __isl_keep isl_basic_map *bmap);
865 __isl_give isl_printer *isl_printer_print_map(
866 __isl_take isl_printer *printer,
867 __isl_keep isl_map *map);
869 #include <isl/union_set.h>
870 __isl_give isl_printer *isl_printer_print_union_set(
871 __isl_take isl_printer *p,
872 __isl_keep isl_union_set *uset);
874 #include <isl/union_map.h>
875 __isl_give isl_printer *isl_printer_print_union_map(
876 __isl_take isl_printer *p,
877 __isl_keep isl_union_map *umap);
879 When called on a file printer, the following function flushes
880 the file. When called on a string printer, the buffer is cleared.
882 __isl_give isl_printer *isl_printer_flush(
883 __isl_take isl_printer *p);
885 =head2 Creating New Sets and Relations
887 C<isl> has functions for creating some standard sets and relations.
891 =item * Empty sets and relations
893 __isl_give isl_basic_set *isl_basic_set_empty(
894 __isl_take isl_space *space);
895 __isl_give isl_basic_map *isl_basic_map_empty(
896 __isl_take isl_space *space);
897 __isl_give isl_set *isl_set_empty(
898 __isl_take isl_space *space);
899 __isl_give isl_map *isl_map_empty(
900 __isl_take isl_space *space);
901 __isl_give isl_union_set *isl_union_set_empty(
902 __isl_take isl_space *space);
903 __isl_give isl_union_map *isl_union_map_empty(
904 __isl_take isl_space *space);
906 For C<isl_union_set>s and C<isl_union_map>s, the space
907 is only used to specify the parameters.
909 =item * Universe sets and relations
911 __isl_give isl_basic_set *isl_basic_set_universe(
912 __isl_take isl_space *space);
913 __isl_give isl_basic_map *isl_basic_map_universe(
914 __isl_take isl_space *space);
915 __isl_give isl_set *isl_set_universe(
916 __isl_take isl_space *space);
917 __isl_give isl_map *isl_map_universe(
918 __isl_take isl_space *space);
919 __isl_give isl_union_set *isl_union_set_universe(
920 __isl_take isl_union_set *uset);
921 __isl_give isl_union_map *isl_union_map_universe(
922 __isl_take isl_union_map *umap);
924 The sets and relations constructed by the functions above
925 contain all integer values, while those constructed by the
926 functions below only contain non-negative values.
928 __isl_give isl_basic_set *isl_basic_set_nat_universe(
929 __isl_take isl_space *space);
930 __isl_give isl_basic_map *isl_basic_map_nat_universe(
931 __isl_take isl_space *space);
932 __isl_give isl_set *isl_set_nat_universe(
933 __isl_take isl_space *space);
934 __isl_give isl_map *isl_map_nat_universe(
935 __isl_take isl_space *space);
937 =item * Identity relations
939 __isl_give isl_basic_map *isl_basic_map_identity(
940 __isl_take isl_space *space);
941 __isl_give isl_map *isl_map_identity(
942 __isl_take isl_space *space);
944 The number of input and output dimensions in C<space> needs
947 =item * Lexicographic order
949 __isl_give isl_map *isl_map_lex_lt(
950 __isl_take isl_space *set_space);
951 __isl_give isl_map *isl_map_lex_le(
952 __isl_take isl_space *set_space);
953 __isl_give isl_map *isl_map_lex_gt(
954 __isl_take isl_space *set_space);
955 __isl_give isl_map *isl_map_lex_ge(
956 __isl_take isl_space *set_space);
957 __isl_give isl_map *isl_map_lex_lt_first(
958 __isl_take isl_space *space, unsigned n);
959 __isl_give isl_map *isl_map_lex_le_first(
960 __isl_take isl_space *space, unsigned n);
961 __isl_give isl_map *isl_map_lex_gt_first(
962 __isl_take isl_space *space, unsigned n);
963 __isl_give isl_map *isl_map_lex_ge_first(
964 __isl_take isl_space *space, unsigned n);
966 The first four functions take a space for a B<set>
967 and return relations that express that the elements in the domain
968 are lexicographically less
969 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
970 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
971 than the elements in the range.
972 The last four functions take a space for a map
973 and return relations that express that the first C<n> dimensions
974 in the domain are lexicographically less
975 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
976 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
977 than the first C<n> dimensions in the range.
981 A basic set or relation can be converted to a set or relation
982 using the following functions.
984 __isl_give isl_set *isl_set_from_basic_set(
985 __isl_take isl_basic_set *bset);
986 __isl_give isl_map *isl_map_from_basic_map(
987 __isl_take isl_basic_map *bmap);
989 Sets and relations can be converted to union sets and relations
990 using the following functions.
992 __isl_give isl_union_map *isl_union_map_from_map(
993 __isl_take isl_map *map);
994 __isl_give isl_union_set *isl_union_set_from_set(
995 __isl_take isl_set *set);
997 The inverse conversions below can only be used if the input
998 union set or relation is known to contain elements in exactly one
1001 __isl_give isl_set *isl_set_from_union_set(
1002 __isl_take isl_union_set *uset);
1003 __isl_give isl_map *isl_map_from_union_map(
1004 __isl_take isl_union_map *umap);
1006 Sets and relations can be copied and freed again using the following
1009 __isl_give isl_basic_set *isl_basic_set_copy(
1010 __isl_keep isl_basic_set *bset);
1011 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1012 __isl_give isl_union_set *isl_union_set_copy(
1013 __isl_keep isl_union_set *uset);
1014 __isl_give isl_basic_map *isl_basic_map_copy(
1015 __isl_keep isl_basic_map *bmap);
1016 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1017 __isl_give isl_union_map *isl_union_map_copy(
1018 __isl_keep isl_union_map *umap);
1019 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1020 void isl_set_free(__isl_take isl_set *set);
1021 void *isl_union_set_free(__isl_take isl_union_set *uset);
1022 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1023 void isl_map_free(__isl_take isl_map *map);
1024 void *isl_union_map_free(__isl_take isl_union_map *umap);
1026 Other sets and relations can be constructed by starting
1027 from a universe set or relation, adding equality and/or
1028 inequality constraints and then projecting out the
1029 existentially quantified variables, if any.
1030 Constraints can be constructed, manipulated and
1031 added to (or removed from) (basic) sets and relations
1032 using the following functions.
1034 #include <isl/constraint.h>
1035 __isl_give isl_constraint *isl_equality_alloc(
1036 __isl_take isl_space *space);
1037 __isl_give isl_constraint *isl_inequality_alloc(
1038 __isl_take isl_space *space);
1039 __isl_give isl_constraint *isl_constraint_set_constant(
1040 __isl_take isl_constraint *constraint, isl_int v);
1041 __isl_give isl_constraint *isl_constraint_set_constant_si(
1042 __isl_take isl_constraint *constraint, int v);
1043 __isl_give isl_constraint *isl_constraint_set_coefficient(
1044 __isl_take isl_constraint *constraint,
1045 enum isl_dim_type type, int pos, isl_int v);
1046 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1047 __isl_take isl_constraint *constraint,
1048 enum isl_dim_type type, int pos, int v);
1049 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1050 __isl_take isl_basic_map *bmap,
1051 __isl_take isl_constraint *constraint);
1052 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1053 __isl_take isl_basic_set *bset,
1054 __isl_take isl_constraint *constraint);
1055 __isl_give isl_map *isl_map_add_constraint(
1056 __isl_take isl_map *map,
1057 __isl_take isl_constraint *constraint);
1058 __isl_give isl_set *isl_set_add_constraint(
1059 __isl_take isl_set *set,
1060 __isl_take isl_constraint *constraint);
1061 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1062 __isl_take isl_basic_set *bset,
1063 __isl_take isl_constraint *constraint);
1065 For example, to create a set containing the even integers
1066 between 10 and 42, you would use the following code.
1071 isl_basic_set *bset;
1074 space = isl_space_set_alloc(ctx, 0, 2);
1075 bset = isl_basic_set_universe(isl_space_copy(space));
1077 c = isl_equality_alloc(isl_space_copy(space));
1078 isl_int_set_si(v, -1);
1079 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1080 isl_int_set_si(v, 2);
1081 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1082 bset = isl_basic_set_add_constraint(bset, c);
1084 c = isl_inequality_alloc(isl_space_copy(space));
1085 isl_int_set_si(v, -10);
1086 isl_constraint_set_constant(c, v);
1087 isl_int_set_si(v, 1);
1088 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1089 bset = isl_basic_set_add_constraint(bset, c);
1091 c = isl_inequality_alloc(space);
1092 isl_int_set_si(v, 42);
1093 isl_constraint_set_constant(c, v);
1094 isl_int_set_si(v, -1);
1095 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1096 bset = isl_basic_set_add_constraint(bset, c);
1098 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1104 isl_basic_set *bset;
1105 bset = isl_basic_set_read_from_str(ctx,
1106 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1108 A basic set or relation can also be constructed from two matrices
1109 describing the equalities and the inequalities.
1111 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1112 __isl_take isl_space *space,
1113 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1114 enum isl_dim_type c1,
1115 enum isl_dim_type c2, enum isl_dim_type c3,
1116 enum isl_dim_type c4);
1117 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1118 __isl_take isl_space *space,
1119 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1120 enum isl_dim_type c1,
1121 enum isl_dim_type c2, enum isl_dim_type c3,
1122 enum isl_dim_type c4, enum isl_dim_type c5);
1124 The C<isl_dim_type> arguments indicate the order in which
1125 different kinds of variables appear in the input matrices
1126 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1127 C<isl_dim_set> and C<isl_dim_div> for sets and
1128 of C<isl_dim_cst>, C<isl_dim_param>,
1129 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1131 A (basic) set or relation can also be constructed from a (piecewise)
1133 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1135 __isl_give isl_basic_map *isl_basic_map_from_aff(
1136 __isl_take isl_aff *aff);
1137 __isl_give isl_set *isl_set_from_pw_aff(
1138 __isl_take isl_pw_aff *pwaff);
1139 __isl_give isl_map *isl_map_from_pw_aff(
1140 __isl_take isl_pw_aff *pwaff);
1141 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1142 __isl_take isl_space *domain_space,
1143 __isl_take isl_aff_list *list);
1145 The C<domain_dim> argument describes the domain of the resulting
1146 basic relation. It is required because the C<list> may consist
1147 of zero affine expressions.
1149 =head2 Inspecting Sets and Relations
1151 Usually, the user should not have to care about the actual constraints
1152 of the sets and maps, but should instead apply the abstract operations
1153 explained in the following sections.
1154 Occasionally, however, it may be required to inspect the individual
1155 coefficients of the constraints. This section explains how to do so.
1156 In these cases, it may also be useful to have C<isl> compute
1157 an explicit representation of the existentially quantified variables.
1159 __isl_give isl_set *isl_set_compute_divs(
1160 __isl_take isl_set *set);
1161 __isl_give isl_map *isl_map_compute_divs(
1162 __isl_take isl_map *map);
1163 __isl_give isl_union_set *isl_union_set_compute_divs(
1164 __isl_take isl_union_set *uset);
1165 __isl_give isl_union_map *isl_union_map_compute_divs(
1166 __isl_take isl_union_map *umap);
1168 This explicit representation defines the existentially quantified
1169 variables as integer divisions of the other variables, possibly
1170 including earlier existentially quantified variables.
1171 An explicitly represented existentially quantified variable therefore
1172 has a unique value when the values of the other variables are known.
1173 If, furthermore, the same existentials, i.e., existentials
1174 with the same explicit representations, should appear in the
1175 same order in each of the disjuncts of a set or map, then the user should call
1176 either of the following functions.
1178 __isl_give isl_set *isl_set_align_divs(
1179 __isl_take isl_set *set);
1180 __isl_give isl_map *isl_map_align_divs(
1181 __isl_take isl_map *map);
1183 Alternatively, the existentially quantified variables can be removed
1184 using the following functions, which compute an overapproximation.
1186 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1187 __isl_take isl_basic_set *bset);
1188 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1189 __isl_take isl_basic_map *bmap);
1190 __isl_give isl_set *isl_set_remove_divs(
1191 __isl_take isl_set *set);
1192 __isl_give isl_map *isl_map_remove_divs(
1193 __isl_take isl_map *map);
1195 To iterate over all the sets or maps in a union set or map, use
1197 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1198 int (*fn)(__isl_take isl_set *set, void *user),
1200 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1201 int (*fn)(__isl_take isl_map *map, void *user),
1204 The number of sets or maps in a union set or map can be obtained
1207 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1208 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1210 To extract the set or map in a given space from a union, use
1212 __isl_give isl_set *isl_union_set_extract_set(
1213 __isl_keep isl_union_set *uset,
1214 __isl_take isl_space *space);
1215 __isl_give isl_map *isl_union_map_extract_map(
1216 __isl_keep isl_union_map *umap,
1217 __isl_take isl_space *space);
1219 To iterate over all the basic sets or maps in a set or map, use
1221 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1222 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1224 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1225 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1228 The callback function C<fn> should return 0 if successful and
1229 -1 if an error occurs. In the latter case, or if any other error
1230 occurs, the above functions will return -1.
1232 It should be noted that C<isl> does not guarantee that
1233 the basic sets or maps passed to C<fn> are disjoint.
1234 If this is required, then the user should call one of
1235 the following functions first.
1237 __isl_give isl_set *isl_set_make_disjoint(
1238 __isl_take isl_set *set);
1239 __isl_give isl_map *isl_map_make_disjoint(
1240 __isl_take isl_map *map);
1242 The number of basic sets in a set can be obtained
1245 int isl_set_n_basic_set(__isl_keep isl_set *set);
1247 To iterate over the constraints of a basic set or map, use
1249 #include <isl/constraint.h>
1251 int isl_basic_map_foreach_constraint(
1252 __isl_keep isl_basic_map *bmap,
1253 int (*fn)(__isl_take isl_constraint *c, void *user),
1255 void *isl_constraint_free(__isl_take isl_constraint *c);
1257 Again, the callback function C<fn> should return 0 if successful and
1258 -1 if an error occurs. In the latter case, or if any other error
1259 occurs, the above functions will return -1.
1260 The constraint C<c> represents either an equality or an inequality.
1261 Use the following function to find out whether a constraint
1262 represents an equality. If not, it represents an inequality.
1264 int isl_constraint_is_equality(
1265 __isl_keep isl_constraint *constraint);
1267 The coefficients of the constraints can be inspected using
1268 the following functions.
1270 void isl_constraint_get_constant(
1271 __isl_keep isl_constraint *constraint, isl_int *v);
1272 void isl_constraint_get_coefficient(
1273 __isl_keep isl_constraint *constraint,
1274 enum isl_dim_type type, int pos, isl_int *v);
1275 int isl_constraint_involves_dims(
1276 __isl_keep isl_constraint *constraint,
1277 enum isl_dim_type type, unsigned first, unsigned n);
1279 The explicit representations of the existentially quantified
1280 variables can be inspected using the following functions.
1281 Note that the user is only allowed to use these functions
1282 if the inspected set or map is the result of a call
1283 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1285 __isl_give isl_div *isl_constraint_div(
1286 __isl_keep isl_constraint *constraint, int pos);
1287 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1288 void isl_div_get_constant(__isl_keep isl_div *div,
1290 void isl_div_get_denominator(__isl_keep isl_div *div,
1292 void isl_div_get_coefficient(__isl_keep isl_div *div,
1293 enum isl_dim_type type, int pos, isl_int *v);
1295 To obtain the constraints of a basic set or map in matrix
1296 form, use the following functions.
1298 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1299 __isl_keep isl_basic_set *bset,
1300 enum isl_dim_type c1, enum isl_dim_type c2,
1301 enum isl_dim_type c3, enum isl_dim_type c4);
1302 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1303 __isl_keep isl_basic_set *bset,
1304 enum isl_dim_type c1, enum isl_dim_type c2,
1305 enum isl_dim_type c3, enum isl_dim_type c4);
1306 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1307 __isl_keep isl_basic_map *bmap,
1308 enum isl_dim_type c1,
1309 enum isl_dim_type c2, enum isl_dim_type c3,
1310 enum isl_dim_type c4, enum isl_dim_type c5);
1311 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1312 __isl_keep isl_basic_map *bmap,
1313 enum isl_dim_type c1,
1314 enum isl_dim_type c2, enum isl_dim_type c3,
1315 enum isl_dim_type c4, enum isl_dim_type c5);
1317 The C<isl_dim_type> arguments dictate the order in which
1318 different kinds of variables appear in the resulting matrix
1319 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1320 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1322 The number of parameters, input, output or set dimensions can
1323 be obtained using the following functions.
1325 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1326 enum isl_dim_type type);
1327 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1328 enum isl_dim_type type);
1329 unsigned isl_set_dim(__isl_keep isl_set *set,
1330 enum isl_dim_type type);
1331 unsigned isl_map_dim(__isl_keep isl_map *map,
1332 enum isl_dim_type type);
1334 To check whether the description of a set or relation depends
1335 on one or more given dimensions, it is not necessary to iterate over all
1336 constraints. Instead the following functions can be used.
1338 int isl_basic_set_involves_dims(
1339 __isl_keep isl_basic_set *bset,
1340 enum isl_dim_type type, unsigned first, unsigned n);
1341 int isl_set_involves_dims(__isl_keep isl_set *set,
1342 enum isl_dim_type type, unsigned first, unsigned n);
1343 int isl_basic_map_involves_dims(
1344 __isl_keep isl_basic_map *bmap,
1345 enum isl_dim_type type, unsigned first, unsigned n);
1346 int isl_map_involves_dims(__isl_keep isl_map *map,
1347 enum isl_dim_type type, unsigned first, unsigned n);
1349 Similarly, the following functions can be used to check whether
1350 a given dimension is involved in any lower or upper bound.
1352 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1353 enum isl_dim_type type, unsigned pos);
1354 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1355 enum isl_dim_type type, unsigned pos);
1357 The identifiers or names of the domain and range spaces of a set
1358 or relation can be read off or set using the following functions.
1360 __isl_give isl_set *isl_set_set_tuple_id(
1361 __isl_take isl_set *set, __isl_take isl_id *id);
1362 __isl_give isl_set *isl_set_reset_tuple_id(
1363 __isl_take isl_set *set);
1364 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1365 __isl_give isl_id *isl_set_get_tuple_id(
1366 __isl_keep isl_set *set);
1367 __isl_give isl_map *isl_map_set_tuple_id(
1368 __isl_take isl_map *map, enum isl_dim_type type,
1369 __isl_take isl_id *id);
1370 __isl_give isl_map *isl_map_reset_tuple_id(
1371 __isl_take isl_map *map, enum isl_dim_type type);
1372 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1373 enum isl_dim_type type);
1374 __isl_give isl_id *isl_map_get_tuple_id(
1375 __isl_keep isl_map *map, enum isl_dim_type type);
1377 const char *isl_basic_set_get_tuple_name(
1378 __isl_keep isl_basic_set *bset);
1379 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1380 __isl_take isl_basic_set *set, const char *s);
1381 const char *isl_set_get_tuple_name(
1382 __isl_keep isl_set *set);
1383 const char *isl_basic_map_get_tuple_name(
1384 __isl_keep isl_basic_map *bmap,
1385 enum isl_dim_type type);
1386 const char *isl_map_get_tuple_name(
1387 __isl_keep isl_map *map,
1388 enum isl_dim_type type);
1390 As with C<isl_space_get_tuple_name>, the value returned points to
1391 an internal data structure.
1392 The identifiers, positions or names of individual dimensions can be
1393 read off using the following functions.
1395 __isl_give isl_set *isl_set_set_dim_id(
1396 __isl_take isl_set *set, enum isl_dim_type type,
1397 unsigned pos, __isl_take isl_id *id);
1398 int isl_set_has_dim_id(__isl_keep isl_set *set,
1399 enum isl_dim_type type, unsigned pos);
1400 __isl_give isl_id *isl_set_get_dim_id(
1401 __isl_keep isl_set *set, enum isl_dim_type type,
1403 __isl_give isl_map *isl_map_set_dim_id(
1404 __isl_take isl_map *map, enum isl_dim_type type,
1405 unsigned pos, __isl_take isl_id *id);
1406 int isl_map_has_dim_id(__isl_keep isl_map *map,
1407 enum isl_dim_type type, unsigned pos);
1408 __isl_give isl_id *isl_map_get_dim_id(
1409 __isl_keep isl_map *map, enum isl_dim_type type,
1412 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1413 enum isl_dim_type type, __isl_keep isl_id *id);
1414 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1415 enum isl_dim_type type, __isl_keep isl_id *id);
1417 const char *isl_constraint_get_dim_name(
1418 __isl_keep isl_constraint *constraint,
1419 enum isl_dim_type type, unsigned pos);
1420 const char *isl_basic_set_get_dim_name(
1421 __isl_keep isl_basic_set *bset,
1422 enum isl_dim_type type, unsigned pos);
1423 const char *isl_set_get_dim_name(
1424 __isl_keep isl_set *set,
1425 enum isl_dim_type type, unsigned pos);
1426 const char *isl_basic_map_get_dim_name(
1427 __isl_keep isl_basic_map *bmap,
1428 enum isl_dim_type type, unsigned pos);
1429 const char *isl_map_get_dim_name(
1430 __isl_keep isl_map *map,
1431 enum isl_dim_type type, unsigned pos);
1433 These functions are mostly useful to obtain the identifiers, positions
1434 or names of the parameters. Identifiers of individual dimensions are
1435 essentially only useful for printing. They are ignored by all other
1436 operations and may not be preserved across those operations.
1440 =head3 Unary Properties
1446 The following functions test whether the given set or relation
1447 contains any integer points. The ``plain'' variants do not perform
1448 any computations, but simply check if the given set or relation
1449 is already known to be empty.
1451 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1452 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1453 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1454 int isl_set_is_empty(__isl_keep isl_set *set);
1455 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1456 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1457 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1458 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1459 int isl_map_is_empty(__isl_keep isl_map *map);
1460 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1462 =item * Universality
1464 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1465 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1466 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1468 =item * Single-valuedness
1470 int isl_map_is_single_valued(__isl_keep isl_map *map);
1471 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1475 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1476 int isl_map_is_injective(__isl_keep isl_map *map);
1477 int isl_union_map_plain_is_injective(
1478 __isl_keep isl_union_map *umap);
1479 int isl_union_map_is_injective(
1480 __isl_keep isl_union_map *umap);
1484 int isl_map_is_bijective(__isl_keep isl_map *map);
1485 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1489 int isl_basic_map_plain_is_fixed(
1490 __isl_keep isl_basic_map *bmap,
1491 enum isl_dim_type type, unsigned pos,
1493 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1494 enum isl_dim_type type, unsigned pos,
1497 Check if the relation obviously lies on a hyperplane where the given dimension
1498 has a fixed value and if so, return that value in C<*val>.
1502 The following functions check whether the domain of the given
1503 (basic) set is a wrapped relation.
1505 int isl_basic_set_is_wrapping(
1506 __isl_keep isl_basic_set *bset);
1507 int isl_set_is_wrapping(__isl_keep isl_set *set);
1509 =item * Internal Product
1511 int isl_basic_map_can_zip(
1512 __isl_keep isl_basic_map *bmap);
1513 int isl_map_can_zip(__isl_keep isl_map *map);
1515 Check whether the product of domain and range of the given relation
1517 i.e., whether both domain and range are nested relations.
1521 =head3 Binary Properties
1527 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1528 __isl_keep isl_set *set2);
1529 int isl_set_is_equal(__isl_keep isl_set *set1,
1530 __isl_keep isl_set *set2);
1531 int isl_union_set_is_equal(
1532 __isl_keep isl_union_set *uset1,
1533 __isl_keep isl_union_set *uset2);
1534 int isl_basic_map_is_equal(
1535 __isl_keep isl_basic_map *bmap1,
1536 __isl_keep isl_basic_map *bmap2);
1537 int isl_map_is_equal(__isl_keep isl_map *map1,
1538 __isl_keep isl_map *map2);
1539 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1540 __isl_keep isl_map *map2);
1541 int isl_union_map_is_equal(
1542 __isl_keep isl_union_map *umap1,
1543 __isl_keep isl_union_map *umap2);
1545 =item * Disjointness
1547 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1548 __isl_keep isl_set *set2);
1552 int isl_set_is_subset(__isl_keep isl_set *set1,
1553 __isl_keep isl_set *set2);
1554 int isl_set_is_strict_subset(
1555 __isl_keep isl_set *set1,
1556 __isl_keep isl_set *set2);
1557 int isl_union_set_is_subset(
1558 __isl_keep isl_union_set *uset1,
1559 __isl_keep isl_union_set *uset2);
1560 int isl_union_set_is_strict_subset(
1561 __isl_keep isl_union_set *uset1,
1562 __isl_keep isl_union_set *uset2);
1563 int isl_basic_map_is_subset(
1564 __isl_keep isl_basic_map *bmap1,
1565 __isl_keep isl_basic_map *bmap2);
1566 int isl_basic_map_is_strict_subset(
1567 __isl_keep isl_basic_map *bmap1,
1568 __isl_keep isl_basic_map *bmap2);
1569 int isl_map_is_subset(
1570 __isl_keep isl_map *map1,
1571 __isl_keep isl_map *map2);
1572 int isl_map_is_strict_subset(
1573 __isl_keep isl_map *map1,
1574 __isl_keep isl_map *map2);
1575 int isl_union_map_is_subset(
1576 __isl_keep isl_union_map *umap1,
1577 __isl_keep isl_union_map *umap2);
1578 int isl_union_map_is_strict_subset(
1579 __isl_keep isl_union_map *umap1,
1580 __isl_keep isl_union_map *umap2);
1584 =head2 Unary Operations
1590 __isl_give isl_set *isl_set_complement(
1591 __isl_take isl_set *set);
1595 __isl_give isl_basic_map *isl_basic_map_reverse(
1596 __isl_take isl_basic_map *bmap);
1597 __isl_give isl_map *isl_map_reverse(
1598 __isl_take isl_map *map);
1599 __isl_give isl_union_map *isl_union_map_reverse(
1600 __isl_take isl_union_map *umap);
1604 __isl_give isl_basic_set *isl_basic_set_project_out(
1605 __isl_take isl_basic_set *bset,
1606 enum isl_dim_type type, unsigned first, unsigned n);
1607 __isl_give isl_basic_map *isl_basic_map_project_out(
1608 __isl_take isl_basic_map *bmap,
1609 enum isl_dim_type type, unsigned first, unsigned n);
1610 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1611 enum isl_dim_type type, unsigned first, unsigned n);
1612 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1613 enum isl_dim_type type, unsigned first, unsigned n);
1614 __isl_give isl_basic_set *isl_basic_map_domain(
1615 __isl_take isl_basic_map *bmap);
1616 __isl_give isl_basic_set *isl_basic_map_range(
1617 __isl_take isl_basic_map *bmap);
1618 __isl_give isl_set *isl_map_domain(
1619 __isl_take isl_map *bmap);
1620 __isl_give isl_set *isl_map_range(
1621 __isl_take isl_map *map);
1622 __isl_give isl_union_set *isl_union_map_domain(
1623 __isl_take isl_union_map *umap);
1624 __isl_give isl_union_set *isl_union_map_range(
1625 __isl_take isl_union_map *umap);
1627 __isl_give isl_basic_map *isl_basic_map_domain_map(
1628 __isl_take isl_basic_map *bmap);
1629 __isl_give isl_basic_map *isl_basic_map_range_map(
1630 __isl_take isl_basic_map *bmap);
1631 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1632 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1633 __isl_give isl_union_map *isl_union_map_domain_map(
1634 __isl_take isl_union_map *umap);
1635 __isl_give isl_union_map *isl_union_map_range_map(
1636 __isl_take isl_union_map *umap);
1638 The functions above construct a (basic, regular or union) relation
1639 that maps (a wrapped version of) the input relation to its domain or range.
1643 __isl_give isl_set *isl_set_eliminate(
1644 __isl_take isl_set *set, enum isl_dim_type type,
1645 unsigned first, unsigned n);
1647 Eliminate the coefficients for the given dimensions from the constraints,
1648 without removing the dimensions.
1652 __isl_give isl_basic_set *isl_basic_set_fix(
1653 __isl_take isl_basic_set *bset,
1654 enum isl_dim_type type, unsigned pos,
1656 __isl_give isl_basic_set *isl_basic_set_fix_si(
1657 __isl_take isl_basic_set *bset,
1658 enum isl_dim_type type, unsigned pos, int value);
1659 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1660 enum isl_dim_type type, unsigned pos,
1662 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1663 enum isl_dim_type type, unsigned pos, int value);
1664 __isl_give isl_basic_map *isl_basic_map_fix_si(
1665 __isl_take isl_basic_map *bmap,
1666 enum isl_dim_type type, unsigned pos, int value);
1667 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1668 enum isl_dim_type type, unsigned pos, int value);
1670 Intersect the set or relation with the hyperplane where the given
1671 dimension has the fixed given value.
1673 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1674 enum isl_dim_type type1, int pos1,
1675 enum isl_dim_type type2, int pos2);
1676 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1677 enum isl_dim_type type1, int pos1,
1678 enum isl_dim_type type2, int pos2);
1680 Intersect the set or relation with the hyperplane where the given
1681 dimensions are equal to each other.
1683 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1684 enum isl_dim_type type1, int pos1,
1685 enum isl_dim_type type2, int pos2);
1687 Intersect the relation with the hyperplane where the given
1688 dimensions have opposite values.
1692 __isl_give isl_map *isl_set_identity(
1693 __isl_take isl_set *set);
1694 __isl_give isl_union_map *isl_union_set_identity(
1695 __isl_take isl_union_set *uset);
1697 Construct an identity relation on the given (union) set.
1701 __isl_give isl_basic_set *isl_basic_map_deltas(
1702 __isl_take isl_basic_map *bmap);
1703 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1704 __isl_give isl_union_set *isl_union_map_deltas(
1705 __isl_take isl_union_map *umap);
1707 These functions return a (basic) set containing the differences
1708 between image elements and corresponding domain elements in the input.
1710 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1711 __isl_take isl_basic_map *bmap);
1712 __isl_give isl_map *isl_map_deltas_map(
1713 __isl_take isl_map *map);
1714 __isl_give isl_union_map *isl_union_map_deltas_map(
1715 __isl_take isl_union_map *umap);
1717 The functions above construct a (basic, regular or union) relation
1718 that maps (a wrapped version of) the input relation to its delta set.
1722 Simplify the representation of a set or relation by trying
1723 to combine pairs of basic sets or relations into a single
1724 basic set or relation.
1726 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1727 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1728 __isl_give isl_union_set *isl_union_set_coalesce(
1729 __isl_take isl_union_set *uset);
1730 __isl_give isl_union_map *isl_union_map_coalesce(
1731 __isl_take isl_union_map *umap);
1733 =item * Detecting equalities
1735 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1736 __isl_take isl_basic_set *bset);
1737 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1738 __isl_take isl_basic_map *bmap);
1739 __isl_give isl_set *isl_set_detect_equalities(
1740 __isl_take isl_set *set);
1741 __isl_give isl_map *isl_map_detect_equalities(
1742 __isl_take isl_map *map);
1743 __isl_give isl_union_set *isl_union_set_detect_equalities(
1744 __isl_take isl_union_set *uset);
1745 __isl_give isl_union_map *isl_union_map_detect_equalities(
1746 __isl_take isl_union_map *umap);
1748 Simplify the representation of a set or relation by detecting implicit
1751 =item * Removing redundant constraints
1753 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1754 __isl_take isl_basic_set *bset);
1755 __isl_give isl_set *isl_set_remove_redundancies(
1756 __isl_take isl_set *set);
1757 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1758 __isl_take isl_basic_map *bmap);
1759 __isl_give isl_map *isl_map_remove_redundancies(
1760 __isl_take isl_map *map);
1764 __isl_give isl_basic_set *isl_set_convex_hull(
1765 __isl_take isl_set *set);
1766 __isl_give isl_basic_map *isl_map_convex_hull(
1767 __isl_take isl_map *map);
1769 If the input set or relation has any existentially quantified
1770 variables, then the result of these operations is currently undefined.
1774 __isl_give isl_basic_set *isl_set_simple_hull(
1775 __isl_take isl_set *set);
1776 __isl_give isl_basic_map *isl_map_simple_hull(
1777 __isl_take isl_map *map);
1778 __isl_give isl_union_map *isl_union_map_simple_hull(
1779 __isl_take isl_union_map *umap);
1781 These functions compute a single basic set or relation
1782 that contains the whole input set or relation.
1783 In particular, the output is described by translates
1784 of the constraints describing the basic sets or relations in the input.
1788 (See \autoref{s:simple hull}.)
1794 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1795 __isl_take isl_basic_set *bset);
1796 __isl_give isl_basic_set *isl_set_affine_hull(
1797 __isl_take isl_set *set);
1798 __isl_give isl_union_set *isl_union_set_affine_hull(
1799 __isl_take isl_union_set *uset);
1800 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1801 __isl_take isl_basic_map *bmap);
1802 __isl_give isl_basic_map *isl_map_affine_hull(
1803 __isl_take isl_map *map);
1804 __isl_give isl_union_map *isl_union_map_affine_hull(
1805 __isl_take isl_union_map *umap);
1807 In case of union sets and relations, the affine hull is computed
1810 =item * Polyhedral hull
1812 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1813 __isl_take isl_set *set);
1814 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1815 __isl_take isl_map *map);
1816 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1817 __isl_take isl_union_set *uset);
1818 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1819 __isl_take isl_union_map *umap);
1821 These functions compute a single basic set or relation
1822 not involving any existentially quantified variables
1823 that contains the whole input set or relation.
1824 In case of union sets and relations, the polyhedral hull is computed
1827 =item * Optimization
1829 #include <isl/ilp.h>
1830 enum isl_lp_result isl_basic_set_max(
1831 __isl_keep isl_basic_set *bset,
1832 __isl_keep isl_aff *obj, isl_int *opt)
1833 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1834 __isl_keep isl_aff *obj, isl_int *opt);
1835 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1836 __isl_keep isl_aff *obj, isl_int *opt);
1838 Compute the minimum or maximum of the integer affine expression C<obj>
1839 over the points in C<set>, returning the result in C<opt>.
1840 The return value may be one of C<isl_lp_error>,
1841 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1843 =item * Parametric optimization
1845 __isl_give isl_pw_aff *isl_set_dim_min(
1846 __isl_take isl_set *set, int pos);
1847 __isl_give isl_pw_aff *isl_set_dim_max(
1848 __isl_take isl_set *set, int pos);
1850 Compute the minimum or maximum of the given set dimension as a function of the
1851 parameters, but independently of the other set dimensions.
1852 For lexicographic optimization, see L<"Lexicographic Optimization">.
1856 The following functions compute either the set of (rational) coefficient
1857 values of valid constraints for the given set or the set of (rational)
1858 values satisfying the constraints with coefficients from the given set.
1859 Internally, these two sets of functions perform essentially the
1860 same operations, except that the set of coefficients is assumed to
1861 be a cone, while the set of values may be any polyhedron.
1862 The current implementation is based on the Farkas lemma and
1863 Fourier-Motzkin elimination, but this may change or be made optional
1864 in future. In particular, future implementations may use different
1865 dualization algorithms or skip the elimination step.
1867 __isl_give isl_basic_set *isl_basic_set_coefficients(
1868 __isl_take isl_basic_set *bset);
1869 __isl_give isl_basic_set *isl_set_coefficients(
1870 __isl_take isl_set *set);
1871 __isl_give isl_union_set *isl_union_set_coefficients(
1872 __isl_take isl_union_set *bset);
1873 __isl_give isl_basic_set *isl_basic_set_solutions(
1874 __isl_take isl_basic_set *bset);
1875 __isl_give isl_basic_set *isl_set_solutions(
1876 __isl_take isl_set *set);
1877 __isl_give isl_union_set *isl_union_set_solutions(
1878 __isl_take isl_union_set *bset);
1882 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1884 __isl_give isl_union_map *isl_union_map_power(
1885 __isl_take isl_union_map *umap, int *exact);
1887 Compute a parametric representation for all positive powers I<k> of C<map>.
1888 The result maps I<k> to a nested relation corresponding to the
1889 I<k>th power of C<map>.
1890 The result may be an overapproximation. If the result is known to be exact,
1891 then C<*exact> is set to C<1>.
1893 =item * Transitive closure
1895 __isl_give isl_map *isl_map_transitive_closure(
1896 __isl_take isl_map *map, int *exact);
1897 __isl_give isl_union_map *isl_union_map_transitive_closure(
1898 __isl_take isl_union_map *umap, int *exact);
1900 Compute the transitive closure of C<map>.
1901 The result may be an overapproximation. If the result is known to be exact,
1902 then C<*exact> is set to C<1>.
1904 =item * Reaching path lengths
1906 __isl_give isl_map *isl_map_reaching_path_lengths(
1907 __isl_take isl_map *map, int *exact);
1909 Compute a relation that maps each element in the range of C<map>
1910 to the lengths of all paths composed of edges in C<map> that
1911 end up in the given element.
1912 The result may be an overapproximation. If the result is known to be exact,
1913 then C<*exact> is set to C<1>.
1914 To compute the I<maximal> path length, the resulting relation
1915 should be postprocessed by C<isl_map_lexmax>.
1916 In particular, if the input relation is a dependence relation
1917 (mapping sources to sinks), then the maximal path length corresponds
1918 to the free schedule.
1919 Note, however, that C<isl_map_lexmax> expects the maximum to be
1920 finite, so if the path lengths are unbounded (possibly due to
1921 the overapproximation), then you will get an error message.
1925 __isl_give isl_basic_set *isl_basic_map_wrap(
1926 __isl_take isl_basic_map *bmap);
1927 __isl_give isl_set *isl_map_wrap(
1928 __isl_take isl_map *map);
1929 __isl_give isl_union_set *isl_union_map_wrap(
1930 __isl_take isl_union_map *umap);
1931 __isl_give isl_basic_map *isl_basic_set_unwrap(
1932 __isl_take isl_basic_set *bset);
1933 __isl_give isl_map *isl_set_unwrap(
1934 __isl_take isl_set *set);
1935 __isl_give isl_union_map *isl_union_set_unwrap(
1936 __isl_take isl_union_set *uset);
1940 Remove any internal structure of domain (and range) of the given
1941 set or relation. If there is any such internal structure in the input,
1942 then the name of the space is also removed.
1944 __isl_give isl_basic_set *isl_basic_set_flatten(
1945 __isl_take isl_basic_set *bset);
1946 __isl_give isl_set *isl_set_flatten(
1947 __isl_take isl_set *set);
1948 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
1949 __isl_take isl_basic_map *bmap);
1950 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1951 __isl_take isl_basic_map *bmap);
1952 __isl_give isl_map *isl_map_flatten_range(
1953 __isl_take isl_map *map);
1954 __isl_give isl_map *isl_map_flatten_domain(
1955 __isl_take isl_map *map);
1956 __isl_give isl_basic_map *isl_basic_map_flatten(
1957 __isl_take isl_basic_map *bmap);
1958 __isl_give isl_map *isl_map_flatten(
1959 __isl_take isl_map *map);
1961 __isl_give isl_map *isl_set_flatten_map(
1962 __isl_take isl_set *set);
1964 The function above constructs a relation
1965 that maps the input set to a flattened version of the set.
1969 Lift the input set to a space with extra dimensions corresponding
1970 to the existentially quantified variables in the input.
1971 In particular, the result lives in a wrapped map where the domain
1972 is the original space and the range corresponds to the original
1973 existentially quantified variables.
1975 __isl_give isl_basic_set *isl_basic_set_lift(
1976 __isl_take isl_basic_set *bset);
1977 __isl_give isl_set *isl_set_lift(
1978 __isl_take isl_set *set);
1979 __isl_give isl_union_set *isl_union_set_lift(
1980 __isl_take isl_union_set *uset);
1982 =item * Internal Product
1984 __isl_give isl_basic_map *isl_basic_map_zip(
1985 __isl_take isl_basic_map *bmap);
1986 __isl_give isl_map *isl_map_zip(
1987 __isl_take isl_map *map);
1988 __isl_give isl_union_map *isl_union_map_zip(
1989 __isl_take isl_union_map *umap);
1991 Given a relation with nested relations for domain and range,
1992 interchange the range of the domain with the domain of the range.
1994 =item * Aligning parameters
1996 __isl_give isl_set *isl_set_align_params(
1997 __isl_take isl_set *set,
1998 __isl_take isl_space *model);
1999 __isl_give isl_map *isl_map_align_params(
2000 __isl_take isl_map *map,
2001 __isl_take isl_space *model);
2003 Change the order of the parameters of the given set or relation
2004 such that the first parameters match those of C<model>.
2005 This may involve the introduction of extra parameters.
2006 All parameters need to be named.
2008 =item * Dimension manipulation
2010 __isl_give isl_set *isl_set_add_dims(
2011 __isl_take isl_set *set,
2012 enum isl_dim_type type, unsigned n);
2013 __isl_give isl_map *isl_map_add_dims(
2014 __isl_take isl_map *map,
2015 enum isl_dim_type type, unsigned n);
2016 __isl_give isl_set *isl_set_insert_dims(
2017 __isl_take isl_set *set,
2018 enum isl_dim_type type, unsigned pos, unsigned n);
2019 __isl_give isl_map *isl_map_insert_dims(
2020 __isl_take isl_map *map,
2021 enum isl_dim_type type, unsigned pos, unsigned n);
2023 It is usually not advisable to directly change the (input or output)
2024 space of a set or a relation as this removes the name and the internal
2025 structure of the space. However, the above functions can be useful
2026 to add new parameters, assuming
2027 C<isl_set_align_params> and C<isl_map_align_params>
2032 =head2 Binary Operations
2034 The two arguments of a binary operation not only need to live
2035 in the same C<isl_ctx>, they currently also need to have
2036 the same (number of) parameters.
2038 =head3 Basic Operations
2042 =item * Intersection
2044 __isl_give isl_basic_set *isl_basic_set_intersect(
2045 __isl_take isl_basic_set *bset1,
2046 __isl_take isl_basic_set *bset2);
2047 __isl_give isl_set *isl_set_intersect_params(
2048 __isl_take isl_set *set,
2049 __isl_take isl_set *params);
2050 __isl_give isl_set *isl_set_intersect(
2051 __isl_take isl_set *set1,
2052 __isl_take isl_set *set2);
2053 __isl_give isl_union_set *isl_union_set_intersect(
2054 __isl_take isl_union_set *uset1,
2055 __isl_take isl_union_set *uset2);
2056 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2057 __isl_take isl_basic_map *bmap,
2058 __isl_take isl_basic_set *bset);
2059 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2060 __isl_take isl_basic_map *bmap,
2061 __isl_take isl_basic_set *bset);
2062 __isl_give isl_basic_map *isl_basic_map_intersect(
2063 __isl_take isl_basic_map *bmap1,
2064 __isl_take isl_basic_map *bmap2);
2065 __isl_give isl_map *isl_map_intersect_params(
2066 __isl_take isl_map *map,
2067 __isl_take isl_set *params);
2068 __isl_give isl_map *isl_map_intersect_domain(
2069 __isl_take isl_map *map,
2070 __isl_take isl_set *set);
2071 __isl_give isl_map *isl_map_intersect_range(
2072 __isl_take isl_map *map,
2073 __isl_take isl_set *set);
2074 __isl_give isl_map *isl_map_intersect(
2075 __isl_take isl_map *map1,
2076 __isl_take isl_map *map2);
2077 __isl_give isl_union_map *isl_union_map_intersect_domain(
2078 __isl_take isl_union_map *umap,
2079 __isl_take isl_union_set *uset);
2080 __isl_give isl_union_map *isl_union_map_intersect_range(
2081 __isl_take isl_union_map *umap,
2082 __isl_take isl_union_set *uset);
2083 __isl_give isl_union_map *isl_union_map_intersect(
2084 __isl_take isl_union_map *umap1,
2085 __isl_take isl_union_map *umap2);
2089 __isl_give isl_set *isl_basic_set_union(
2090 __isl_take isl_basic_set *bset1,
2091 __isl_take isl_basic_set *bset2);
2092 __isl_give isl_map *isl_basic_map_union(
2093 __isl_take isl_basic_map *bmap1,
2094 __isl_take isl_basic_map *bmap2);
2095 __isl_give isl_set *isl_set_union(
2096 __isl_take isl_set *set1,
2097 __isl_take isl_set *set2);
2098 __isl_give isl_map *isl_map_union(
2099 __isl_take isl_map *map1,
2100 __isl_take isl_map *map2);
2101 __isl_give isl_union_set *isl_union_set_union(
2102 __isl_take isl_union_set *uset1,
2103 __isl_take isl_union_set *uset2);
2104 __isl_give isl_union_map *isl_union_map_union(
2105 __isl_take isl_union_map *umap1,
2106 __isl_take isl_union_map *umap2);
2108 =item * Set difference
2110 __isl_give isl_set *isl_set_subtract(
2111 __isl_take isl_set *set1,
2112 __isl_take isl_set *set2);
2113 __isl_give isl_map *isl_map_subtract(
2114 __isl_take isl_map *map1,
2115 __isl_take isl_map *map2);
2116 __isl_give isl_union_set *isl_union_set_subtract(
2117 __isl_take isl_union_set *uset1,
2118 __isl_take isl_union_set *uset2);
2119 __isl_give isl_union_map *isl_union_map_subtract(
2120 __isl_take isl_union_map *umap1,
2121 __isl_take isl_union_map *umap2);
2125 __isl_give isl_basic_set *isl_basic_set_apply(
2126 __isl_take isl_basic_set *bset,
2127 __isl_take isl_basic_map *bmap);
2128 __isl_give isl_set *isl_set_apply(
2129 __isl_take isl_set *set,
2130 __isl_take isl_map *map);
2131 __isl_give isl_union_set *isl_union_set_apply(
2132 __isl_take isl_union_set *uset,
2133 __isl_take isl_union_map *umap);
2134 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2135 __isl_take isl_basic_map *bmap1,
2136 __isl_take isl_basic_map *bmap2);
2137 __isl_give isl_basic_map *isl_basic_map_apply_range(
2138 __isl_take isl_basic_map *bmap1,
2139 __isl_take isl_basic_map *bmap2);
2140 __isl_give isl_map *isl_map_apply_domain(
2141 __isl_take isl_map *map1,
2142 __isl_take isl_map *map2);
2143 __isl_give isl_union_map *isl_union_map_apply_domain(
2144 __isl_take isl_union_map *umap1,
2145 __isl_take isl_union_map *umap2);
2146 __isl_give isl_map *isl_map_apply_range(
2147 __isl_take isl_map *map1,
2148 __isl_take isl_map *map2);
2149 __isl_give isl_union_map *isl_union_map_apply_range(
2150 __isl_take isl_union_map *umap1,
2151 __isl_take isl_union_map *umap2);
2153 =item * Cartesian Product
2155 __isl_give isl_set *isl_set_product(
2156 __isl_take isl_set *set1,
2157 __isl_take isl_set *set2);
2158 __isl_give isl_union_set *isl_union_set_product(
2159 __isl_take isl_union_set *uset1,
2160 __isl_take isl_union_set *uset2);
2161 __isl_give isl_basic_map *isl_basic_map_domain_product(
2162 __isl_take isl_basic_map *bmap1,
2163 __isl_take isl_basic_map *bmap2);
2164 __isl_give isl_basic_map *isl_basic_map_range_product(
2165 __isl_take isl_basic_map *bmap1,
2166 __isl_take isl_basic_map *bmap2);
2167 __isl_give isl_map *isl_map_domain_product(
2168 __isl_take isl_map *map1,
2169 __isl_take isl_map *map2);
2170 __isl_give isl_map *isl_map_range_product(
2171 __isl_take isl_map *map1,
2172 __isl_take isl_map *map2);
2173 __isl_give isl_union_map *isl_union_map_range_product(
2174 __isl_take isl_union_map *umap1,
2175 __isl_take isl_union_map *umap2);
2176 __isl_give isl_map *isl_map_product(
2177 __isl_take isl_map *map1,
2178 __isl_take isl_map *map2);
2179 __isl_give isl_union_map *isl_union_map_product(
2180 __isl_take isl_union_map *umap1,
2181 __isl_take isl_union_map *umap2);
2183 The above functions compute the cross product of the given
2184 sets or relations. The domains and ranges of the results
2185 are wrapped maps between domains and ranges of the inputs.
2186 To obtain a ``flat'' product, use the following functions
2189 __isl_give isl_basic_set *isl_basic_set_flat_product(
2190 __isl_take isl_basic_set *bset1,
2191 __isl_take isl_basic_set *bset2);
2192 __isl_give isl_set *isl_set_flat_product(
2193 __isl_take isl_set *set1,
2194 __isl_take isl_set *set2);
2195 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2196 __isl_take isl_basic_map *bmap1,
2197 __isl_take isl_basic_map *bmap2);
2198 __isl_give isl_map *isl_map_flat_domain_product(
2199 __isl_take isl_map *map1,
2200 __isl_take isl_map *map2);
2201 __isl_give isl_map *isl_map_flat_range_product(
2202 __isl_take isl_map *map1,
2203 __isl_take isl_map *map2);
2204 __isl_give isl_union_map *isl_union_map_flat_range_product(
2205 __isl_take isl_union_map *umap1,
2206 __isl_take isl_union_map *umap2);
2207 __isl_give isl_basic_map *isl_basic_map_flat_product(
2208 __isl_take isl_basic_map *bmap1,
2209 __isl_take isl_basic_map *bmap2);
2210 __isl_give isl_map *isl_map_flat_product(
2211 __isl_take isl_map *map1,
2212 __isl_take isl_map *map2);
2214 =item * Simplification
2216 __isl_give isl_basic_set *isl_basic_set_gist(
2217 __isl_take isl_basic_set *bset,
2218 __isl_take isl_basic_set *context);
2219 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2220 __isl_take isl_set *context);
2221 __isl_give isl_union_set *isl_union_set_gist(
2222 __isl_take isl_union_set *uset,
2223 __isl_take isl_union_set *context);
2224 __isl_give isl_basic_map *isl_basic_map_gist(
2225 __isl_take isl_basic_map *bmap,
2226 __isl_take isl_basic_map *context);
2227 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2228 __isl_take isl_map *context);
2229 __isl_give isl_union_map *isl_union_map_gist(
2230 __isl_take isl_union_map *umap,
2231 __isl_take isl_union_map *context);
2233 The gist operation returns a set or relation that has the
2234 same intersection with the context as the input set or relation.
2235 Any implicit equality in the intersection is made explicit in the result,
2236 while all inequalities that are redundant with respect to the intersection
2238 In case of union sets and relations, the gist operation is performed
2243 =head3 Lexicographic Optimization
2245 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2246 the following functions
2247 compute a set that contains the lexicographic minimum or maximum
2248 of the elements in C<set> (or C<bset>) for those values of the parameters
2249 that satisfy C<dom>.
2250 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2251 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2253 In other words, the union of the parameter values
2254 for which the result is non-empty and of C<*empty>
2257 __isl_give isl_set *isl_basic_set_partial_lexmin(
2258 __isl_take isl_basic_set *bset,
2259 __isl_take isl_basic_set *dom,
2260 __isl_give isl_set **empty);
2261 __isl_give isl_set *isl_basic_set_partial_lexmax(
2262 __isl_take isl_basic_set *bset,
2263 __isl_take isl_basic_set *dom,
2264 __isl_give isl_set **empty);
2265 __isl_give isl_set *isl_set_partial_lexmin(
2266 __isl_take isl_set *set, __isl_take isl_set *dom,
2267 __isl_give isl_set **empty);
2268 __isl_give isl_set *isl_set_partial_lexmax(
2269 __isl_take isl_set *set, __isl_take isl_set *dom,
2270 __isl_give isl_set **empty);
2272 Given a (basic) set C<set> (or C<bset>), the following functions simply
2273 return a set containing the lexicographic minimum or maximum
2274 of the elements in C<set> (or C<bset>).
2275 In case of union sets, the optimum is computed per space.
2277 __isl_give isl_set *isl_basic_set_lexmin(
2278 __isl_take isl_basic_set *bset);
2279 __isl_give isl_set *isl_basic_set_lexmax(
2280 __isl_take isl_basic_set *bset);
2281 __isl_give isl_set *isl_set_lexmin(
2282 __isl_take isl_set *set);
2283 __isl_give isl_set *isl_set_lexmax(
2284 __isl_take isl_set *set);
2285 __isl_give isl_union_set *isl_union_set_lexmin(
2286 __isl_take isl_union_set *uset);
2287 __isl_give isl_union_set *isl_union_set_lexmax(
2288 __isl_take isl_union_set *uset);
2290 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2291 the following functions
2292 compute a relation that maps each element of C<dom>
2293 to the single lexicographic minimum or maximum
2294 of the elements that are associated to that same
2295 element in C<map> (or C<bmap>).
2296 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2297 that contains the elements in C<dom> that do not map
2298 to any elements in C<map> (or C<bmap>).
2299 In other words, the union of the domain of the result and of C<*empty>
2302 __isl_give isl_map *isl_basic_map_partial_lexmax(
2303 __isl_take isl_basic_map *bmap,
2304 __isl_take isl_basic_set *dom,
2305 __isl_give isl_set **empty);
2306 __isl_give isl_map *isl_basic_map_partial_lexmin(
2307 __isl_take isl_basic_map *bmap,
2308 __isl_take isl_basic_set *dom,
2309 __isl_give isl_set **empty);
2310 __isl_give isl_map *isl_map_partial_lexmax(
2311 __isl_take isl_map *map, __isl_take isl_set *dom,
2312 __isl_give isl_set **empty);
2313 __isl_give isl_map *isl_map_partial_lexmin(
2314 __isl_take isl_map *map, __isl_take isl_set *dom,
2315 __isl_give isl_set **empty);
2317 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2318 return a map mapping each element in the domain of
2319 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2320 of all elements associated to that element.
2321 In case of union relations, the optimum is computed per space.
2323 __isl_give isl_map *isl_basic_map_lexmin(
2324 __isl_take isl_basic_map *bmap);
2325 __isl_give isl_map *isl_basic_map_lexmax(
2326 __isl_take isl_basic_map *bmap);
2327 __isl_give isl_map *isl_map_lexmin(
2328 __isl_take isl_map *map);
2329 __isl_give isl_map *isl_map_lexmax(
2330 __isl_take isl_map *map);
2331 __isl_give isl_union_map *isl_union_map_lexmin(
2332 __isl_take isl_union_map *umap);
2333 __isl_give isl_union_map *isl_union_map_lexmax(
2334 __isl_take isl_union_map *umap);
2338 Lists are defined over several element types, including
2339 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2340 Here we take lists of C<isl_set>s as an example.
2341 Lists can be created, copied and freed using the following functions.
2343 #include <isl/list.h>
2344 __isl_give isl_set_list *isl_set_list_from_set(
2345 __isl_take isl_set *el);
2346 __isl_give isl_set_list *isl_set_list_alloc(
2347 isl_ctx *ctx, int n);
2348 __isl_give isl_set_list *isl_set_list_copy(
2349 __isl_keep isl_set_list *list);
2350 __isl_give isl_set_list *isl_set_list_add(
2351 __isl_take isl_set_list *list,
2352 __isl_take isl_set *el);
2353 __isl_give isl_set_list *isl_set_list_concat(
2354 __isl_take isl_set_list *list1,
2355 __isl_take isl_set_list *list2);
2356 void *isl_set_list_free(__isl_take isl_set_list *list);
2358 C<isl_set_list_alloc> creates an empty list with a capacity for
2359 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2362 Lists can be inspected using the following functions.
2364 #include <isl/list.h>
2365 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2366 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2367 __isl_give isl_set *isl_set_list_get_set(
2368 __isl_keep isl_set_list *list, int index);
2369 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2370 int (*fn)(__isl_take isl_set *el, void *user),
2373 Lists can be printed using
2375 #include <isl/list.h>
2376 __isl_give isl_printer *isl_printer_print_set_list(
2377 __isl_take isl_printer *p,
2378 __isl_keep isl_set_list *list);
2382 Matrices can be created, copied and freed using the following functions.
2384 #include <isl/mat.h>
2385 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2386 unsigned n_row, unsigned n_col);
2387 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2388 void isl_mat_free(__isl_take isl_mat *mat);
2390 Note that the elements of a newly created matrix may have arbitrary values.
2391 The elements can be changed and inspected using the following functions.
2393 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2394 int isl_mat_rows(__isl_keep isl_mat *mat);
2395 int isl_mat_cols(__isl_keep isl_mat *mat);
2396 int isl_mat_get_element(__isl_keep isl_mat *mat,
2397 int row, int col, isl_int *v);
2398 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2399 int row, int col, isl_int v);
2400 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2401 int row, int col, int v);
2403 C<isl_mat_get_element> will return a negative value if anything went wrong.
2404 In that case, the value of C<*v> is undefined.
2406 The following function can be used to compute the (right) inverse
2407 of a matrix, i.e., a matrix such that the product of the original
2408 and the inverse (in that order) is a multiple of the identity matrix.
2409 The input matrix is assumed to be of full row-rank.
2411 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2413 The following function can be used to compute the (right) kernel
2414 (or null space) of a matrix, i.e., a matrix such that the product of
2415 the original and the kernel (in that order) is the zero matrix.
2417 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2419 =head2 Piecewise Quasi Affine Expressions
2421 The zero quasi affine expression can be created using
2423 __isl_give isl_aff *isl_aff_zero(
2424 __isl_take isl_local_space *ls);
2426 A quasi affine expression can also be initialized from an C<isl_div>:
2428 #include <isl/div.h>
2429 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2431 An empty piecewise quasi affine expression (one with no cells)
2432 or a piecewise quasi affine expression with a single cell can
2433 be created using the following functions.
2435 #include <isl/aff.h>
2436 __isl_give isl_pw_aff *isl_pw_aff_empty(
2437 __isl_take isl_space *space);
2438 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2439 __isl_take isl_set *set, __isl_take isl_aff *aff);
2440 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2441 __isl_take isl_aff *aff);
2443 Quasi affine expressions can be copied and freed using
2445 #include <isl/aff.h>
2446 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2447 void *isl_aff_free(__isl_take isl_aff *aff);
2449 __isl_give isl_pw_aff *isl_pw_aff_copy(
2450 __isl_keep isl_pw_aff *pwaff);
2451 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2453 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2454 using the following function. The constraint is required to have
2455 a non-zero coefficient for the specified dimension.
2457 #include <isl/constraint.h>
2458 __isl_give isl_aff *isl_constraint_get_bound(
2459 __isl_keep isl_constraint *constraint,
2460 enum isl_dim_type type, int pos);
2462 The entire affine expression of the constraint can also be extracted
2463 using the following function.
2465 #include <isl/constraint.h>
2466 __isl_give isl_aff *isl_constraint_get_aff(
2467 __isl_keep isl_constraint *constraint);
2469 Conversely, an equality constraint equating
2470 the affine expression to zero or an inequality constraint enforcing
2471 the affine expression to be non-negative, can be constructed using
2473 __isl_give isl_constraint *isl_equality_from_aff(
2474 __isl_take isl_aff *aff);
2475 __isl_give isl_constraint *isl_inequality_from_aff(
2476 __isl_take isl_aff *aff);
2478 The expression can be inspected using
2480 #include <isl/aff.h>
2481 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2482 int isl_aff_dim(__isl_keep isl_aff *aff,
2483 enum isl_dim_type type);
2484 __isl_give isl_local_space *isl_aff_get_local_space(
2485 __isl_keep isl_aff *aff);
2486 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2487 enum isl_dim_type type, unsigned pos);
2488 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2490 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2491 enum isl_dim_type type, int pos, isl_int *v);
2492 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2494 __isl_give isl_div *isl_aff_get_div(
2495 __isl_keep isl_aff *aff, int pos);
2497 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2498 int (*fn)(__isl_take isl_set *set,
2499 __isl_take isl_aff *aff,
2500 void *user), void *user);
2502 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2503 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2505 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2506 enum isl_dim_type type, unsigned first, unsigned n);
2507 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2508 enum isl_dim_type type, unsigned first, unsigned n);
2510 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2511 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2512 enum isl_dim_type type);
2513 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2515 It can be modified using
2517 #include <isl/aff.h>
2518 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2519 __isl_take isl_pw_aff *pwaff,
2520 __isl_take isl_id *id);
2521 __isl_give isl_aff *isl_aff_set_dim_name(
2522 __isl_take isl_aff *aff, enum isl_dim_type type,
2523 unsigned pos, const char *s);
2524 __isl_give isl_aff *isl_aff_set_constant(
2525 __isl_take isl_aff *aff, isl_int v);
2526 __isl_give isl_aff *isl_aff_set_constant_si(
2527 __isl_take isl_aff *aff, int v);
2528 __isl_give isl_aff *isl_aff_set_coefficient(
2529 __isl_take isl_aff *aff,
2530 enum isl_dim_type type, int pos, isl_int v);
2531 __isl_give isl_aff *isl_aff_set_coefficient_si(
2532 __isl_take isl_aff *aff,
2533 enum isl_dim_type type, int pos, int v);
2534 __isl_give isl_aff *isl_aff_set_denominator(
2535 __isl_take isl_aff *aff, isl_int v);
2537 __isl_give isl_aff *isl_aff_add_constant(
2538 __isl_take isl_aff *aff, isl_int v);
2539 __isl_give isl_aff *isl_aff_add_constant_si(
2540 __isl_take isl_aff *aff, int v);
2541 __isl_give isl_aff *isl_aff_add_coefficient(
2542 __isl_take isl_aff *aff,
2543 enum isl_dim_type type, int pos, isl_int v);
2544 __isl_give isl_aff *isl_aff_add_coefficient_si(
2545 __isl_take isl_aff *aff,
2546 enum isl_dim_type type, int pos, int v);
2548 __isl_give isl_aff *isl_aff_insert_dims(
2549 __isl_take isl_aff *aff,
2550 enum isl_dim_type type, unsigned first, unsigned n);
2551 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2552 __isl_take isl_pw_aff *pwaff,
2553 enum isl_dim_type type, unsigned first, unsigned n);
2554 __isl_give isl_aff *isl_aff_add_dims(
2555 __isl_take isl_aff *aff,
2556 enum isl_dim_type type, unsigned n);
2557 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2558 __isl_take isl_pw_aff *pwaff,
2559 enum isl_dim_type type, unsigned n);
2560 __isl_give isl_aff *isl_aff_drop_dims(
2561 __isl_take isl_aff *aff,
2562 enum isl_dim_type type, unsigned first, unsigned n);
2563 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2564 __isl_take isl_pw_aff *pwaff,
2565 enum isl_dim_type type, unsigned first, unsigned n);
2567 Note that the C<set_constant> and C<set_coefficient> functions
2568 set the I<numerator> of the constant or coefficient, while
2569 C<add_constant> and C<add_coefficient> add an integer value to
2570 the possibly rational constant or coefficient.
2572 To check whether an affine expressions is obviously zero
2573 or obviously equal to some other affine expression, use
2575 #include <isl/aff.h>
2576 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2577 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2578 __isl_keep isl_aff *aff2);
2582 #include <isl/aff.h>
2583 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2584 __isl_take isl_aff *aff2);
2585 __isl_give isl_pw_aff *isl_pw_aff_add(
2586 __isl_take isl_pw_aff *pwaff1,
2587 __isl_take isl_pw_aff *pwaff2);
2588 __isl_give isl_pw_aff *isl_pw_aff_min(
2589 __isl_take isl_pw_aff *pwaff1,
2590 __isl_take isl_pw_aff *pwaff2);
2591 __isl_give isl_pw_aff *isl_pw_aff_max(
2592 __isl_take isl_pw_aff *pwaff1,
2593 __isl_take isl_pw_aff *pwaff2);
2594 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2595 __isl_take isl_aff *aff2);
2596 __isl_give isl_pw_aff *isl_pw_aff_sub(
2597 __isl_take isl_pw_aff *pwaff1,
2598 __isl_take isl_pw_aff *pwaff2);
2599 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2600 __isl_give isl_pw_aff *isl_pw_aff_neg(
2601 __isl_take isl_pw_aff *pwaff);
2602 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2603 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2604 __isl_take isl_pw_aff *pwaff);
2605 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2606 __isl_give isl_pw_aff *isl_pw_aff_floor(
2607 __isl_take isl_pw_aff *pwaff);
2608 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2610 __isl_give isl_pw_aff *isl_pw_aff_mod(
2611 __isl_take isl_pw_aff *pwaff, isl_int mod);
2612 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2614 __isl_give isl_pw_aff *isl_pw_aff_scale(
2615 __isl_take isl_pw_aff *pwaff, isl_int f);
2616 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2618 __isl_give isl_aff *isl_aff_scale_down_ui(
2619 __isl_take isl_aff *aff, unsigned f);
2620 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2621 __isl_take isl_pw_aff *pwaff, isl_int f);
2623 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2624 __isl_take isl_pw_aff_list *list);
2625 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2626 __isl_take isl_pw_aff_list *list);
2628 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2629 __isl_take isl_pw_aff *pwqp);
2631 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2632 __isl_take isl_pw_aff *pwaff,
2633 __isl_take isl_space *model);
2635 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2636 __isl_take isl_set *context);
2637 __isl_give isl_pw_aff *isl_pw_aff_gist(
2638 __isl_take isl_pw_aff *pwaff,
2639 __isl_take isl_set *context);
2641 __isl_give isl_set *isl_pw_aff_domain(
2642 __isl_take isl_pw_aff *pwaff);
2644 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2645 __isl_take isl_aff *aff2);
2646 __isl_give isl_pw_aff *isl_pw_aff_mul(
2647 __isl_take isl_pw_aff *pwaff1,
2648 __isl_take isl_pw_aff *pwaff2);
2650 When multiplying two affine expressions, at least one of the two needs
2653 #include <isl/aff.h>
2654 __isl_give isl_basic_set *isl_aff_le_basic_set(
2655 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2656 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2657 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2658 __isl_give isl_set *isl_pw_aff_eq_set(
2659 __isl_take isl_pw_aff *pwaff1,
2660 __isl_take isl_pw_aff *pwaff2);
2661 __isl_give isl_set *isl_pw_aff_ne_set(
2662 __isl_take isl_pw_aff *pwaff1,
2663 __isl_take isl_pw_aff *pwaff2);
2664 __isl_give isl_set *isl_pw_aff_le_set(
2665 __isl_take isl_pw_aff *pwaff1,
2666 __isl_take isl_pw_aff *pwaff2);
2667 __isl_give isl_set *isl_pw_aff_lt_set(
2668 __isl_take isl_pw_aff *pwaff1,
2669 __isl_take isl_pw_aff *pwaff2);
2670 __isl_give isl_set *isl_pw_aff_ge_set(
2671 __isl_take isl_pw_aff *pwaff1,
2672 __isl_take isl_pw_aff *pwaff2);
2673 __isl_give isl_set *isl_pw_aff_gt_set(
2674 __isl_take isl_pw_aff *pwaff1,
2675 __isl_take isl_pw_aff *pwaff2);
2677 __isl_give isl_set *isl_pw_aff_list_eq_set(
2678 __isl_take isl_pw_aff_list *list1,
2679 __isl_take isl_pw_aff_list *list2);
2680 __isl_give isl_set *isl_pw_aff_list_ne_set(
2681 __isl_take isl_pw_aff_list *list1,
2682 __isl_take isl_pw_aff_list *list2);
2683 __isl_give isl_set *isl_pw_aff_list_le_set(
2684 __isl_take isl_pw_aff_list *list1,
2685 __isl_take isl_pw_aff_list *list2);
2686 __isl_give isl_set *isl_pw_aff_list_lt_set(
2687 __isl_take isl_pw_aff_list *list1,
2688 __isl_take isl_pw_aff_list *list2);
2689 __isl_give isl_set *isl_pw_aff_list_ge_set(
2690 __isl_take isl_pw_aff_list *list1,
2691 __isl_take isl_pw_aff_list *list2);
2692 __isl_give isl_set *isl_pw_aff_list_gt_set(
2693 __isl_take isl_pw_aff_list *list1,
2694 __isl_take isl_pw_aff_list *list2);
2696 The function C<isl_aff_ge_basic_set> returns a basic set
2697 containing those elements in the shared space
2698 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2699 The function C<isl_aff_ge_set> returns a set
2700 containing those elements in the shared domain
2701 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2702 The functions operating on C<isl_pw_aff_list> apply the corresponding
2703 C<isl_pw_aff> function to each pair of elements in the two lists.
2705 #include <isl/aff.h>
2706 __isl_give isl_set *isl_pw_aff_nonneg_set(
2707 __isl_take isl_pw_aff *pwaff);
2708 __isl_give isl_set *isl_pw_aff_zero_set(
2709 __isl_take isl_pw_aff *pwaff);
2710 __isl_give isl_set *isl_pw_aff_non_zero_set(
2711 __isl_take isl_pw_aff *pwaff);
2713 The function C<isl_pw_aff_nonneg_set> returns a set
2714 containing those elements in the domain
2715 of C<pwaff> where C<pwaff> is non-negative.
2717 #include <isl/aff.h>
2718 __isl_give isl_pw_aff *isl_pw_aff_cond(
2719 __isl_take isl_set *cond,
2720 __isl_take isl_pw_aff *pwaff_true,
2721 __isl_take isl_pw_aff *pwaff_false);
2723 The function C<isl_pw_aff_cond> performs a conditional operator
2724 and returns an expression that is equal to C<pwaff_true>
2725 for elements in C<cond> and equal to C<pwaff_false> for elements
2728 #include <isl/aff.h>
2729 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2730 __isl_take isl_pw_aff *pwaff1,
2731 __isl_take isl_pw_aff *pwaff2);
2732 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2733 __isl_take isl_pw_aff *pwaff1,
2734 __isl_take isl_pw_aff *pwaff2);
2736 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2737 expression with a domain that is the union of those of C<pwaff1> and
2738 C<pwaff2> and such that on each cell, the quasi-affine expression is
2739 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2740 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2741 associated expression is the defined one.
2743 An expression can be printed using
2745 #include <isl/aff.h>
2746 __isl_give isl_printer *isl_printer_print_aff(
2747 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2749 __isl_give isl_printer *isl_printer_print_pw_aff(
2750 __isl_take isl_printer *p,
2751 __isl_keep isl_pw_aff *pwaff);
2755 Points are elements of a set. They can be used to construct
2756 simple sets (boxes) or they can be used to represent the
2757 individual elements of a set.
2758 The zero point (the origin) can be created using
2760 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2762 The coordinates of a point can be inspected, set and changed
2765 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2766 enum isl_dim_type type, int pos, isl_int *v);
2767 __isl_give isl_point *isl_point_set_coordinate(
2768 __isl_take isl_point *pnt,
2769 enum isl_dim_type type, int pos, isl_int v);
2771 __isl_give isl_point *isl_point_add_ui(
2772 __isl_take isl_point *pnt,
2773 enum isl_dim_type type, int pos, unsigned val);
2774 __isl_give isl_point *isl_point_sub_ui(
2775 __isl_take isl_point *pnt,
2776 enum isl_dim_type type, int pos, unsigned val);
2778 Other properties can be obtained using
2780 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2782 Points can be copied or freed using
2784 __isl_give isl_point *isl_point_copy(
2785 __isl_keep isl_point *pnt);
2786 void isl_point_free(__isl_take isl_point *pnt);
2788 A singleton set can be created from a point using
2790 __isl_give isl_basic_set *isl_basic_set_from_point(
2791 __isl_take isl_point *pnt);
2792 __isl_give isl_set *isl_set_from_point(
2793 __isl_take isl_point *pnt);
2795 and a box can be created from two opposite extremal points using
2797 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2798 __isl_take isl_point *pnt1,
2799 __isl_take isl_point *pnt2);
2800 __isl_give isl_set *isl_set_box_from_points(
2801 __isl_take isl_point *pnt1,
2802 __isl_take isl_point *pnt2);
2804 All elements of a B<bounded> (union) set can be enumerated using
2805 the following functions.
2807 int isl_set_foreach_point(__isl_keep isl_set *set,
2808 int (*fn)(__isl_take isl_point *pnt, void *user),
2810 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2811 int (*fn)(__isl_take isl_point *pnt, void *user),
2814 The function C<fn> is called for each integer point in
2815 C<set> with as second argument the last argument of
2816 the C<isl_set_foreach_point> call. The function C<fn>
2817 should return C<0> on success and C<-1> on failure.
2818 In the latter case, C<isl_set_foreach_point> will stop
2819 enumerating and return C<-1> as well.
2820 If the enumeration is performed successfully and to completion,
2821 then C<isl_set_foreach_point> returns C<0>.
2823 To obtain a single point of a (basic) set, use
2825 __isl_give isl_point *isl_basic_set_sample_point(
2826 __isl_take isl_basic_set *bset);
2827 __isl_give isl_point *isl_set_sample_point(
2828 __isl_take isl_set *set);
2830 If C<set> does not contain any (integer) points, then the
2831 resulting point will be ``void'', a property that can be
2834 int isl_point_is_void(__isl_keep isl_point *pnt);
2836 =head2 Piecewise Quasipolynomials
2838 A piecewise quasipolynomial is a particular kind of function that maps
2839 a parametric point to a rational value.
2840 More specifically, a quasipolynomial is a polynomial expression in greatest
2841 integer parts of affine expressions of parameters and variables.
2842 A piecewise quasipolynomial is a subdivision of a given parametric
2843 domain into disjoint cells with a quasipolynomial associated to
2844 each cell. The value of the piecewise quasipolynomial at a given
2845 point is the value of the quasipolynomial associated to the cell
2846 that contains the point. Outside of the union of cells,
2847 the value is assumed to be zero.
2848 For example, the piecewise quasipolynomial
2850 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2852 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2853 A given piecewise quasipolynomial has a fixed domain dimension.
2854 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2855 defined over different domains.
2856 Piecewise quasipolynomials are mainly used by the C<barvinok>
2857 library for representing the number of elements in a parametric set or map.
2858 For example, the piecewise quasipolynomial above represents
2859 the number of points in the map
2861 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2863 =head3 Printing (Piecewise) Quasipolynomials
2865 Quasipolynomials and piecewise quasipolynomials can be printed
2866 using the following functions.
2868 __isl_give isl_printer *isl_printer_print_qpolynomial(
2869 __isl_take isl_printer *p,
2870 __isl_keep isl_qpolynomial *qp);
2872 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2873 __isl_take isl_printer *p,
2874 __isl_keep isl_pw_qpolynomial *pwqp);
2876 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2877 __isl_take isl_printer *p,
2878 __isl_keep isl_union_pw_qpolynomial *upwqp);
2880 The output format of the printer
2881 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2882 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2884 In case of printing in C<ISL_FORMAT_C>, the user may want
2885 to set the names of all dimensions
2887 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2888 __isl_take isl_qpolynomial *qp,
2889 enum isl_dim_type type, unsigned pos,
2891 __isl_give isl_pw_qpolynomial *
2892 isl_pw_qpolynomial_set_dim_name(
2893 __isl_take isl_pw_qpolynomial *pwqp,
2894 enum isl_dim_type type, unsigned pos,
2897 =head3 Creating New (Piecewise) Quasipolynomials
2899 Some simple quasipolynomials can be created using the following functions.
2900 More complicated quasipolynomials can be created by applying
2901 operations such as addition and multiplication
2902 on the resulting quasipolynomials
2904 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2905 __isl_take isl_space *dim);
2906 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2907 __isl_take isl_space *dim);
2908 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2909 __isl_take isl_space *dim);
2910 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2911 __isl_take isl_space *dim);
2912 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2913 __isl_take isl_space *dim);
2914 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2915 __isl_take isl_space *dim,
2916 const isl_int n, const isl_int d);
2917 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2918 __isl_take isl_div *div);
2919 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2920 __isl_take isl_space *dim,
2921 enum isl_dim_type type, unsigned pos);
2922 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2923 __isl_take isl_aff *aff);
2925 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2926 with a single cell can be created using the following functions.
2927 Multiple of these single cell piecewise quasipolynomials can
2928 be combined to create more complicated piecewise quasipolynomials.
2930 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2931 __isl_take isl_space *space);
2932 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2933 __isl_take isl_set *set,
2934 __isl_take isl_qpolynomial *qp);
2935 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2936 __isl_take isl_qpolynomial *qp);
2937 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2938 __isl_take isl_pw_aff *pwaff);
2940 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2941 __isl_take isl_space *space);
2942 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2943 __isl_take isl_pw_qpolynomial *pwqp);
2944 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2945 __isl_take isl_union_pw_qpolynomial *upwqp,
2946 __isl_take isl_pw_qpolynomial *pwqp);
2948 Quasipolynomials can be copied and freed again using the following
2951 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2952 __isl_keep isl_qpolynomial *qp);
2953 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2955 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2956 __isl_keep isl_pw_qpolynomial *pwqp);
2957 void *isl_pw_qpolynomial_free(
2958 __isl_take isl_pw_qpolynomial *pwqp);
2960 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2961 __isl_keep isl_union_pw_qpolynomial *upwqp);
2962 void isl_union_pw_qpolynomial_free(
2963 __isl_take isl_union_pw_qpolynomial *upwqp);
2965 =head3 Inspecting (Piecewise) Quasipolynomials
2967 To iterate over all piecewise quasipolynomials in a union
2968 piecewise quasipolynomial, use the following function
2970 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2971 __isl_keep isl_union_pw_qpolynomial *upwqp,
2972 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2975 To extract the piecewise quasipolynomial in a given space from a union, use
2977 __isl_give isl_pw_qpolynomial *
2978 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2979 __isl_keep isl_union_pw_qpolynomial *upwqp,
2980 __isl_take isl_space *space);
2982 To iterate over the cells in a piecewise quasipolynomial,
2983 use either of the following two functions
2985 int isl_pw_qpolynomial_foreach_piece(
2986 __isl_keep isl_pw_qpolynomial *pwqp,
2987 int (*fn)(__isl_take isl_set *set,
2988 __isl_take isl_qpolynomial *qp,
2989 void *user), void *user);
2990 int isl_pw_qpolynomial_foreach_lifted_piece(
2991 __isl_keep isl_pw_qpolynomial *pwqp,
2992 int (*fn)(__isl_take isl_set *set,
2993 __isl_take isl_qpolynomial *qp,
2994 void *user), void *user);
2996 As usual, the function C<fn> should return C<0> on success
2997 and C<-1> on failure. The difference between
2998 C<isl_pw_qpolynomial_foreach_piece> and
2999 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3000 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3001 compute unique representations for all existentially quantified
3002 variables and then turn these existentially quantified variables
3003 into extra set variables, adapting the associated quasipolynomial
3004 accordingly. This means that the C<set> passed to C<fn>
3005 will not have any existentially quantified variables, but that
3006 the dimensions of the sets may be different for different
3007 invocations of C<fn>.
3009 To iterate over all terms in a quasipolynomial,
3012 int isl_qpolynomial_foreach_term(
3013 __isl_keep isl_qpolynomial *qp,
3014 int (*fn)(__isl_take isl_term *term,
3015 void *user), void *user);
3017 The terms themselves can be inspected and freed using
3020 unsigned isl_term_dim(__isl_keep isl_term *term,
3021 enum isl_dim_type type);
3022 void isl_term_get_num(__isl_keep isl_term *term,
3024 void isl_term_get_den(__isl_keep isl_term *term,
3026 int isl_term_get_exp(__isl_keep isl_term *term,
3027 enum isl_dim_type type, unsigned pos);
3028 __isl_give isl_div *isl_term_get_div(
3029 __isl_keep isl_term *term, unsigned pos);
3030 void isl_term_free(__isl_take isl_term *term);
3032 Each term is a product of parameters, set variables and
3033 integer divisions. The function C<isl_term_get_exp>
3034 returns the exponent of a given dimensions in the given term.
3035 The C<isl_int>s in the arguments of C<isl_term_get_num>
3036 and C<isl_term_get_den> need to have been initialized
3037 using C<isl_int_init> before calling these functions.
3039 =head3 Properties of (Piecewise) Quasipolynomials
3041 To check whether a quasipolynomial is actually a constant,
3042 use the following function.
3044 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3045 isl_int *n, isl_int *d);
3047 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3048 then the numerator and denominator of the constant
3049 are returned in C<*n> and C<*d>, respectively.
3051 =head3 Operations on (Piecewise) Quasipolynomials
3053 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3054 __isl_take isl_qpolynomial *qp, isl_int v);
3055 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3056 __isl_take isl_qpolynomial *qp);
3057 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3058 __isl_take isl_qpolynomial *qp1,
3059 __isl_take isl_qpolynomial *qp2);
3060 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3061 __isl_take isl_qpolynomial *qp1,
3062 __isl_take isl_qpolynomial *qp2);
3063 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3064 __isl_take isl_qpolynomial *qp1,
3065 __isl_take isl_qpolynomial *qp2);
3066 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3067 __isl_take isl_qpolynomial *qp, unsigned exponent);
3069 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3070 __isl_take isl_pw_qpolynomial *pwqp1,
3071 __isl_take isl_pw_qpolynomial *pwqp2);
3072 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3073 __isl_take isl_pw_qpolynomial *pwqp1,
3074 __isl_take isl_pw_qpolynomial *pwqp2);
3075 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3076 __isl_take isl_pw_qpolynomial *pwqp1,
3077 __isl_take isl_pw_qpolynomial *pwqp2);
3078 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3079 __isl_take isl_pw_qpolynomial *pwqp);
3080 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3081 __isl_take isl_pw_qpolynomial *pwqp1,
3082 __isl_take isl_pw_qpolynomial *pwqp2);
3083 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3084 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3086 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3087 __isl_take isl_union_pw_qpolynomial *upwqp1,
3088 __isl_take isl_union_pw_qpolynomial *upwqp2);
3089 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3090 __isl_take isl_union_pw_qpolynomial *upwqp1,
3091 __isl_take isl_union_pw_qpolynomial *upwqp2);
3092 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3093 __isl_take isl_union_pw_qpolynomial *upwqp1,
3094 __isl_take isl_union_pw_qpolynomial *upwqp2);
3096 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3097 __isl_take isl_pw_qpolynomial *pwqp,
3098 __isl_take isl_point *pnt);
3100 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3101 __isl_take isl_union_pw_qpolynomial *upwqp,
3102 __isl_take isl_point *pnt);
3104 __isl_give isl_set *isl_pw_qpolynomial_domain(
3105 __isl_take isl_pw_qpolynomial *pwqp);
3106 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3107 __isl_take isl_pw_qpolynomial *pwpq,
3108 __isl_take isl_set *set);
3110 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3111 __isl_take isl_union_pw_qpolynomial *upwqp);
3112 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3113 __isl_take isl_union_pw_qpolynomial *upwpq,
3114 __isl_take isl_union_set *uset);
3116 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3117 __isl_take isl_qpolynomial *qp,
3118 __isl_take isl_space *model);
3120 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3121 __isl_take isl_union_pw_qpolynomial *upwqp);
3123 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3124 __isl_take isl_qpolynomial *qp,
3125 __isl_take isl_set *context);
3127 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3128 __isl_take isl_pw_qpolynomial *pwqp,
3129 __isl_take isl_set *context);
3131 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3132 __isl_take isl_union_pw_qpolynomial *upwqp,
3133 __isl_take isl_union_set *context);
3135 The gist operation applies the gist operation to each of
3136 the cells in the domain of the input piecewise quasipolynomial.
3137 The context is also exploited
3138 to simplify the quasipolynomials associated to each cell.
3140 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3141 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3142 __isl_give isl_union_pw_qpolynomial *
3143 isl_union_pw_qpolynomial_to_polynomial(
3144 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3146 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3147 the polynomial will be an overapproximation. If C<sign> is negative,
3148 it will be an underapproximation. If C<sign> is zero, the approximation
3149 will lie somewhere in between.
3151 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3153 A piecewise quasipolynomial reduction is a piecewise
3154 reduction (or fold) of quasipolynomials.
3155 In particular, the reduction can be maximum or a minimum.
3156 The objects are mainly used to represent the result of
3157 an upper or lower bound on a quasipolynomial over its domain,
3158 i.e., as the result of the following function.
3160 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3161 __isl_take isl_pw_qpolynomial *pwqp,
3162 enum isl_fold type, int *tight);
3164 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3165 __isl_take isl_union_pw_qpolynomial *upwqp,
3166 enum isl_fold type, int *tight);
3168 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3169 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3170 is the returned bound is known be tight, i.e., for each value
3171 of the parameters there is at least
3172 one element in the domain that reaches the bound.
3173 If the domain of C<pwqp> is not wrapping, then the bound is computed
3174 over all elements in that domain and the result has a purely parametric
3175 domain. If the domain of C<pwqp> is wrapping, then the bound is
3176 computed over the range of the wrapped relation. The domain of the
3177 wrapped relation becomes the domain of the result.
3179 A (piecewise) quasipolynomial reduction can be copied or freed using the
3180 following functions.
3182 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3183 __isl_keep isl_qpolynomial_fold *fold);
3184 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3185 __isl_keep isl_pw_qpolynomial_fold *pwf);
3186 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3187 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3188 void isl_qpolynomial_fold_free(
3189 __isl_take isl_qpolynomial_fold *fold);
3190 void *isl_pw_qpolynomial_fold_free(
3191 __isl_take isl_pw_qpolynomial_fold *pwf);
3192 void isl_union_pw_qpolynomial_fold_free(
3193 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3195 =head3 Printing Piecewise Quasipolynomial Reductions
3197 Piecewise quasipolynomial reductions can be printed
3198 using the following function.
3200 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3201 __isl_take isl_printer *p,
3202 __isl_keep isl_pw_qpolynomial_fold *pwf);
3203 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3204 __isl_take isl_printer *p,
3205 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3207 For C<isl_printer_print_pw_qpolynomial_fold>,
3208 output format of the printer
3209 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3210 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3211 output format of the printer
3212 needs to be set to C<ISL_FORMAT_ISL>.
3213 In case of printing in C<ISL_FORMAT_C>, the user may want
3214 to set the names of all dimensions
3216 __isl_give isl_pw_qpolynomial_fold *
3217 isl_pw_qpolynomial_fold_set_dim_name(
3218 __isl_take isl_pw_qpolynomial_fold *pwf,
3219 enum isl_dim_type type, unsigned pos,
3222 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3224 To iterate over all piecewise quasipolynomial reductions in a union
3225 piecewise quasipolynomial reduction, use the following function
3227 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3228 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3229 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3230 void *user), void *user);
3232 To iterate over the cells in a piecewise quasipolynomial reduction,
3233 use either of the following two functions
3235 int isl_pw_qpolynomial_fold_foreach_piece(
3236 __isl_keep isl_pw_qpolynomial_fold *pwf,
3237 int (*fn)(__isl_take isl_set *set,
3238 __isl_take isl_qpolynomial_fold *fold,
3239 void *user), void *user);
3240 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3241 __isl_keep isl_pw_qpolynomial_fold *pwf,
3242 int (*fn)(__isl_take isl_set *set,
3243 __isl_take isl_qpolynomial_fold *fold,
3244 void *user), void *user);
3246 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3247 of the difference between these two functions.
3249 To iterate over all quasipolynomials in a reduction, use
3251 int isl_qpolynomial_fold_foreach_qpolynomial(
3252 __isl_keep isl_qpolynomial_fold *fold,
3253 int (*fn)(__isl_take isl_qpolynomial *qp,
3254 void *user), void *user);
3256 =head3 Operations on Piecewise Quasipolynomial Reductions
3258 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3259 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3261 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3262 __isl_take isl_pw_qpolynomial_fold *pwf1,
3263 __isl_take isl_pw_qpolynomial_fold *pwf2);
3265 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3266 __isl_take isl_pw_qpolynomial_fold *pwf1,
3267 __isl_take isl_pw_qpolynomial_fold *pwf2);
3269 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3270 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3271 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3273 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3274 __isl_take isl_pw_qpolynomial_fold *pwf,
3275 __isl_take isl_point *pnt);
3277 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3278 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3279 __isl_take isl_point *pnt);
3281 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3282 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3283 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3284 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3285 __isl_take isl_union_set *uset);
3287 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3288 __isl_take isl_pw_qpolynomial_fold *pwf);
3290 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3291 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3293 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3294 __isl_take isl_pw_qpolynomial_fold *pwf,
3295 __isl_take isl_set *context);
3297 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3298 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3299 __isl_take isl_union_set *context);
3301 The gist operation applies the gist operation to each of
3302 the cells in the domain of the input piecewise quasipolynomial reduction.
3303 In future, the operation will also exploit the context
3304 to simplify the quasipolynomial reductions associated to each cell.
3306 __isl_give isl_pw_qpolynomial_fold *
3307 isl_set_apply_pw_qpolynomial_fold(
3308 __isl_take isl_set *set,
3309 __isl_take isl_pw_qpolynomial_fold *pwf,
3311 __isl_give isl_pw_qpolynomial_fold *
3312 isl_map_apply_pw_qpolynomial_fold(
3313 __isl_take isl_map *map,
3314 __isl_take isl_pw_qpolynomial_fold *pwf,
3316 __isl_give isl_union_pw_qpolynomial_fold *
3317 isl_union_set_apply_union_pw_qpolynomial_fold(
3318 __isl_take isl_union_set *uset,
3319 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3321 __isl_give isl_union_pw_qpolynomial_fold *
3322 isl_union_map_apply_union_pw_qpolynomial_fold(
3323 __isl_take isl_union_map *umap,
3324 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3327 The functions taking a map
3328 compose the given map with the given piecewise quasipolynomial reduction.
3329 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3330 over all elements in the intersection of the range of the map
3331 and the domain of the piecewise quasipolynomial reduction
3332 as a function of an element in the domain of the map.
3333 The functions taking a set compute a bound over all elements in the
3334 intersection of the set and the domain of the
3335 piecewise quasipolynomial reduction.
3337 =head2 Dependence Analysis
3339 C<isl> contains specialized functionality for performing
3340 array dataflow analysis. That is, given a I<sink> access relation
3341 and a collection of possible I<source> access relations,
3342 C<isl> can compute relations that describe
3343 for each iteration of the sink access, which iteration
3344 of which of the source access relations was the last
3345 to access the same data element before the given iteration
3347 To compute standard flow dependences, the sink should be
3348 a read, while the sources should be writes.
3349 If any of the source accesses are marked as being I<may>
3350 accesses, then there will be a dependence to the last
3351 I<must> access B<and> to any I<may> access that follows
3352 this last I<must> access.
3353 In particular, if I<all> sources are I<may> accesses,
3354 then memory based dependence analysis is performed.
3355 If, on the other hand, all sources are I<must> accesses,
3356 then value based dependence analysis is performed.
3358 #include <isl/flow.h>
3360 typedef int (*isl_access_level_before)(void *first, void *second);
3362 __isl_give isl_access_info *isl_access_info_alloc(
3363 __isl_take isl_map *sink,
3364 void *sink_user, isl_access_level_before fn,
3366 __isl_give isl_access_info *isl_access_info_add_source(
3367 __isl_take isl_access_info *acc,
3368 __isl_take isl_map *source, int must,
3370 void isl_access_info_free(__isl_take isl_access_info *acc);
3372 __isl_give isl_flow *isl_access_info_compute_flow(
3373 __isl_take isl_access_info *acc);
3375 int isl_flow_foreach(__isl_keep isl_flow *deps,
3376 int (*fn)(__isl_take isl_map *dep, int must,
3377 void *dep_user, void *user),
3379 __isl_give isl_map *isl_flow_get_no_source(
3380 __isl_keep isl_flow *deps, int must);
3381 void isl_flow_free(__isl_take isl_flow *deps);
3383 The function C<isl_access_info_compute_flow> performs the actual
3384 dependence analysis. The other functions are used to construct
3385 the input for this function or to read off the output.
3387 The input is collected in an C<isl_access_info>, which can
3388 be created through a call to C<isl_access_info_alloc>.
3389 The arguments to this functions are the sink access relation
3390 C<sink>, a token C<sink_user> used to identify the sink
3391 access to the user, a callback function for specifying the
3392 relative order of source and sink accesses, and the number
3393 of source access relations that will be added.
3394 The callback function has type C<int (*)(void *first, void *second)>.
3395 The function is called with two user supplied tokens identifying
3396 either a source or the sink and it should return the shared nesting
3397 level and the relative order of the two accesses.
3398 In particular, let I<n> be the number of loops shared by
3399 the two accesses. If C<first> precedes C<second> textually,
3400 then the function should return I<2 * n + 1>; otherwise,
3401 it should return I<2 * n>.
3402 The sources can be added to the C<isl_access_info> by performing
3403 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3404 C<must> indicates whether the source is a I<must> access
3405 or a I<may> access. Note that a multi-valued access relation
3406 should only be marked I<must> if every iteration in the domain
3407 of the relation accesses I<all> elements in its image.
3408 The C<source_user> token is again used to identify
3409 the source access. The range of the source access relation
3410 C<source> should have the same dimension as the range
3411 of the sink access relation.
3412 The C<isl_access_info_free> function should usually not be
3413 called explicitly, because it is called implicitly by
3414 C<isl_access_info_compute_flow>.
3416 The result of the dependence analysis is collected in an
3417 C<isl_flow>. There may be elements of
3418 the sink access for which no preceding source access could be
3419 found or for which all preceding sources are I<may> accesses.
3420 The relations containing these elements can be obtained through
3421 calls to C<isl_flow_get_no_source>, the first with C<must> set
3422 and the second with C<must> unset.
3423 In the case of standard flow dependence analysis,
3424 with the sink a read and the sources I<must> writes,
3425 the first relation corresponds to the reads from uninitialized
3426 array elements and the second relation is empty.
3427 The actual flow dependences can be extracted using
3428 C<isl_flow_foreach>. This function will call the user-specified
3429 callback function C<fn> for each B<non-empty> dependence between
3430 a source and the sink. The callback function is called
3431 with four arguments, the actual flow dependence relation
3432 mapping source iterations to sink iterations, a boolean that
3433 indicates whether it is a I<must> or I<may> dependence, a token
3434 identifying the source and an additional C<void *> with value
3435 equal to the third argument of the C<isl_flow_foreach> call.
3436 A dependence is marked I<must> if it originates from a I<must>
3437 source and if it is not followed by any I<may> sources.
3439 After finishing with an C<isl_flow>, the user should call
3440 C<isl_flow_free> to free all associated memory.
3442 A higher-level interface to dependence analysis is provided
3443 by the following function.
3445 #include <isl/flow.h>
3447 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3448 __isl_take isl_union_map *must_source,
3449 __isl_take isl_union_map *may_source,
3450 __isl_take isl_union_map *schedule,
3451 __isl_give isl_union_map **must_dep,
3452 __isl_give isl_union_map **may_dep,
3453 __isl_give isl_union_map **must_no_source,
3454 __isl_give isl_union_map **may_no_source);
3456 The arrays are identified by the tuple names of the ranges
3457 of the accesses. The iteration domains by the tuple names
3458 of the domains of the accesses and of the schedule.
3459 The relative order of the iteration domains is given by the
3460 schedule. The relations returned through C<must_no_source>
3461 and C<may_no_source> are subsets of C<sink>.
3462 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3463 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3464 any of the other arguments is treated as an error.
3468 B<The functionality described in this section is fairly new
3469 and may be subject to change.>
3471 The following function can be used to compute a schedule
3472 for a union of domains. The generated schedule respects
3473 all C<validity> dependences. That is, all dependence distances
3474 over these dependences in the scheduled space are lexicographically
3475 positive. The generated schedule schedule also tries to minimize
3476 the dependence distances over C<proximity> dependences.
3477 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3478 for groups of domains where the dependence distances have only
3479 non-negative values.
3480 The algorithm used to construct the schedule is similar to that
3483 #include <isl/schedule.h>
3484 __isl_give isl_schedule *isl_union_set_compute_schedule(
3485 __isl_take isl_union_set *domain,
3486 __isl_take isl_union_map *validity,
3487 __isl_take isl_union_map *proximity);
3488 void *isl_schedule_free(__isl_take isl_schedule *sched);
3490 A mapping from the domains to the scheduled space can be obtained
3491 from an C<isl_schedule> using the following function.
3493 __isl_give isl_union_map *isl_schedule_get_map(
3494 __isl_keep isl_schedule *sched);
3496 A representation of the schedule can be printed using
3498 __isl_give isl_printer *isl_printer_print_schedule(
3499 __isl_take isl_printer *p,
3500 __isl_keep isl_schedule *schedule);
3502 A representation of the schedule as a forest of bands can be obtained
3503 using the following function.
3505 __isl_give isl_band_list *isl_schedule_get_band_forest(
3506 __isl_keep isl_schedule *schedule);
3508 The list can be manipulated as explained in L<"Lists">.
3509 The bands inside the list can be copied and freed using the following
3512 #include <isl/band.h>
3513 __isl_give isl_band *isl_band_copy(
3514 __isl_keep isl_band *band);
3515 void *isl_band_free(__isl_take isl_band *band);
3517 Each band contains zero or more scheduling dimensions.
3518 These are referred to as the members of the band.
3519 The section of the schedule that corresponds to the band is
3520 referred to as the partial schedule of the band.
3521 For those nodes that participate in a band, the outer scheduling
3522 dimensions form the prefix schedule, while the inner scheduling
3523 dimensions form the suffix schedule.
3524 That is, if we take a cut of the band forest, then the union of
3525 the concatenations of the prefix, partial and suffix schedules of
3526 each band in the cut is equal to the entire schedule (modulo
3527 some possible padding at the end with zero scheduling dimensions).
3528 The properties of a band can be inspected using the following functions.
3530 #include <isl/band.h>
3531 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3533 int isl_band_has_children(__isl_keep isl_band *band);
3534 __isl_give isl_band_list *isl_band_get_children(
3535 __isl_keep isl_band *band);
3537 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3538 __isl_keep isl_band *band);
3539 __isl_give isl_union_map *isl_band_get_partial_schedule(
3540 __isl_keep isl_band *band);
3541 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3542 __isl_keep isl_band *band);
3544 int isl_band_n_member(__isl_keep isl_band *band);
3545 int isl_band_member_is_zero_distance(
3546 __isl_keep isl_band *band, int pos);
3548 Note that a scheduling dimension is considered to be ``zero
3549 distance'' if it does not carry any proximity dependences
3551 That is, if the dependence distances of the proximity
3552 dependences are all zero in that direction (for fixed
3553 iterations of outer bands).
3555 A representation of the band can be printed using
3557 #include <isl/band.h>
3558 __isl_give isl_printer *isl_printer_print_band(
3559 __isl_take isl_printer *p,
3560 __isl_keep isl_band *band);
3562 =head2 Parametric Vertex Enumeration
3564 The parametric vertex enumeration described in this section
3565 is mainly intended to be used internally and by the C<barvinok>
3568 #include <isl/vertices.h>
3569 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3570 __isl_keep isl_basic_set *bset);
3572 The function C<isl_basic_set_compute_vertices> performs the
3573 actual computation of the parametric vertices and the chamber
3574 decomposition and store the result in an C<isl_vertices> object.
3575 This information can be queried by either iterating over all
3576 the vertices or iterating over all the chambers or cells
3577 and then iterating over all vertices that are active on the chamber.
3579 int isl_vertices_foreach_vertex(
3580 __isl_keep isl_vertices *vertices,
3581 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3584 int isl_vertices_foreach_cell(
3585 __isl_keep isl_vertices *vertices,
3586 int (*fn)(__isl_take isl_cell *cell, void *user),
3588 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3589 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3592 Other operations that can be performed on an C<isl_vertices> object are
3595 isl_ctx *isl_vertices_get_ctx(
3596 __isl_keep isl_vertices *vertices);
3597 int isl_vertices_get_n_vertices(
3598 __isl_keep isl_vertices *vertices);
3599 void isl_vertices_free(__isl_take isl_vertices *vertices);
3601 Vertices can be inspected and destroyed using the following functions.
3603 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3604 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3605 __isl_give isl_basic_set *isl_vertex_get_domain(
3606 __isl_keep isl_vertex *vertex);
3607 __isl_give isl_basic_set *isl_vertex_get_expr(
3608 __isl_keep isl_vertex *vertex);
3609 void isl_vertex_free(__isl_take isl_vertex *vertex);
3611 C<isl_vertex_get_expr> returns a singleton parametric set describing
3612 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3614 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3615 B<rational> basic sets, so they should mainly be used for inspection
3616 and should not be mixed with integer sets.
3618 Chambers can be inspected and destroyed using the following functions.
3620 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3621 __isl_give isl_basic_set *isl_cell_get_domain(
3622 __isl_keep isl_cell *cell);
3623 void isl_cell_free(__isl_take isl_cell *cell);
3627 Although C<isl> is mainly meant to be used as a library,
3628 it also contains some basic applications that use some
3629 of the functionality of C<isl>.
3630 The input may be specified in either the L<isl format>
3631 or the L<PolyLib format>.
3633 =head2 C<isl_polyhedron_sample>
3635 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3636 an integer element of the polyhedron, if there is any.
3637 The first column in the output is the denominator and is always
3638 equal to 1. If the polyhedron contains no integer points,
3639 then a vector of length zero is printed.
3643 C<isl_pip> takes the same input as the C<example> program
3644 from the C<piplib> distribution, i.e., a set of constraints
3645 on the parameters, a line containing only -1 and finally a set
3646 of constraints on a parametric polyhedron.
3647 The coefficients of the parameters appear in the last columns
3648 (but before the final constant column).
3649 The output is the lexicographic minimum of the parametric polyhedron.
3650 As C<isl> currently does not have its own output format, the output
3651 is just a dump of the internal state.
3653 =head2 C<isl_polyhedron_minimize>
3655 C<isl_polyhedron_minimize> computes the minimum of some linear
3656 or affine objective function over the integer points in a polyhedron.
3657 If an affine objective function
3658 is given, then the constant should appear in the last column.
3660 =head2 C<isl_polytope_scan>
3662 Given a polytope, C<isl_polytope_scan> prints
3663 all integer points in the polytope.