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_params_alloc(isl_ctx *ctx,
471 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
472 unsigned nparam, unsigned dim);
473 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
474 void isl_space_free(__isl_take isl_space *space);
475 unsigned isl_space_dim(__isl_keep isl_space *space,
476 enum isl_dim_type type);
478 The space used for creating a parameter domain
479 needs to be created using C<isl_space_params_alloc>.
480 For other sets, the space
481 needs to be created using C<isl_space_set_alloc>, while
482 for a relation, the space
483 needs to be created using C<isl_space_alloc>.
484 C<isl_space_dim> can be used
485 to find out the number of dimensions of each type in
486 a space, where type may be
487 C<isl_dim_param>, C<isl_dim_in> (only for relations),
488 C<isl_dim_out> (only for relations), C<isl_dim_set>
489 (only for sets) or C<isl_dim_all>.
491 It is often useful to create objects that live in the
492 same space as some other object. This can be accomplished
493 by creating the new objects
494 (see L<Creating New Sets and Relations> or
495 L<Creating New (Piecewise) Quasipolynomials>) based on the space
496 of the original object.
499 __isl_give isl_space *isl_basic_set_get_space(
500 __isl_keep isl_basic_set *bset);
501 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
503 #include <isl/union_set.h>
504 __isl_give isl_space *isl_union_set_get_space(
505 __isl_keep isl_union_set *uset);
508 __isl_give isl_space *isl_basic_map_get_space(
509 __isl_keep isl_basic_map *bmap);
510 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
512 #include <isl/union_map.h>
513 __isl_give isl_space *isl_union_map_get_space(
514 __isl_keep isl_union_map *umap);
516 #include <isl/constraint.h>
517 __isl_give isl_space *isl_constraint_get_space(
518 __isl_keep isl_constraint *constraint);
520 #include <isl/polynomial.h>
521 __isl_give isl_space *isl_qpolynomial_get_space(
522 __isl_keep isl_qpolynomial *qp);
523 __isl_give isl_space *isl_qpolynomial_fold_get_space(
524 __isl_keep isl_qpolynomial_fold *fold);
525 __isl_give isl_space *isl_pw_qpolynomial_get_space(
526 __isl_keep isl_pw_qpolynomial *pwqp);
527 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
528 __isl_keep isl_union_pw_qpolynomial *upwqp);
529 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
530 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
533 __isl_give isl_space *isl_aff_get_space(
534 __isl_keep isl_aff *aff);
535 __isl_give isl_space *isl_pw_aff_get_space(
536 __isl_keep isl_pw_aff *pwaff);
538 #include <isl/point.h>
539 __isl_give isl_space *isl_point_get_space(
540 __isl_keep isl_point *pnt);
542 The identifiers or names of the individual dimensions may be set or read off
543 using the following functions.
545 #include <isl/space.h>
546 __isl_give isl_space *isl_space_set_dim_id(
547 __isl_take isl_space *space,
548 enum isl_dim_type type, unsigned pos,
549 __isl_take isl_id *id);
550 int isl_space_has_dim_id(__isl_keep isl_space *space,
551 enum isl_dim_type type, unsigned pos);
552 __isl_give isl_id *isl_space_get_dim_id(
553 __isl_keep isl_space *space,
554 enum isl_dim_type type, unsigned pos);
555 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
556 enum isl_dim_type type, unsigned pos,
557 __isl_keep const char *name);
558 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
559 enum isl_dim_type type, unsigned pos);
561 Note that C<isl_space_get_name> returns a pointer to some internal
562 data structure, so the result can only be used while the
563 corresponding C<isl_space> is alive.
564 Also note that every function that operates on two sets or relations
565 requires that both arguments have the same parameters. This also
566 means that if one of the arguments has named parameters, then the
567 other needs to have named parameters too and the names need to match.
568 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
569 arguments may have different parameters (as long as they are named),
570 in which case the result will have as parameters the union of the parameters of
573 Given the identifier of a dimension (typically a parameter),
574 its position can be obtained from the following function.
576 #include <isl/space.h>
577 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
578 enum isl_dim_type type, __isl_keep isl_id *id);
580 The identifiers or names of entire spaces may be set or read off
581 using the following functions.
583 #include <isl/space.h>
584 __isl_give isl_space *isl_space_set_tuple_id(
585 __isl_take isl_space *space,
586 enum isl_dim_type type, __isl_take isl_id *id);
587 __isl_give isl_space *isl_space_reset_tuple_id(
588 __isl_take isl_space *space, enum isl_dim_type type);
589 int isl_space_has_tuple_id(__isl_keep isl_space *space,
590 enum isl_dim_type type);
591 __isl_give isl_id *isl_space_get_tuple_id(
592 __isl_keep isl_space *space, enum isl_dim_type type);
593 __isl_give isl_space *isl_space_set_tuple_name(
594 __isl_take isl_space *space,
595 enum isl_dim_type type, const char *s);
596 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
597 enum isl_dim_type type);
599 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
600 or C<isl_dim_set>. As with C<isl_space_get_name>,
601 the C<isl_space_get_tuple_name> function returns a pointer to some internal
603 Binary operations require the corresponding spaces of their arguments
604 to have the same name.
606 Spaces can be nested. In particular, the domain of a set or
607 the domain or range of a relation can be a nested relation.
608 The following functions can be used to construct and deconstruct
611 #include <isl/space.h>
612 int isl_space_is_wrapping(__isl_keep isl_space *space);
613 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
614 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
616 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
617 be the space of a set, while that of
618 C<isl_space_wrap> should be the space of a relation.
619 Conversely, the output of C<isl_space_unwrap> is the space
620 of a relation, while that of C<isl_space_wrap> is the space of a set.
622 Spaces can be created from other spaces
623 using the following functions.
625 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
626 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
627 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
628 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
629 __isl_give isl_space *isl_space_params(
630 __isl_take isl_space *space);
631 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
632 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
633 __isl_take isl_space *right);
634 __isl_give isl_space *isl_space_align_params(
635 __isl_take isl_space *space1, __isl_take isl_space *space2)
636 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
637 enum isl_dim_type type, unsigned pos, unsigned n);
638 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
639 enum isl_dim_type type, unsigned n);
640 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
641 enum isl_dim_type type, unsigned first, unsigned n);
642 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
643 enum isl_dim_type dst_type, unsigned dst_pos,
644 enum isl_dim_type src_type, unsigned src_pos,
646 __isl_give isl_space *isl_space_map_from_set(
647 __isl_take isl_space *space);
648 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
650 Note that if dimensions are added or removed from a space, then
651 the name and the internal structure are lost.
655 A local space is essentially a space with
656 zero or more existentially quantified variables.
657 The local space of a basic set or relation can be obtained
658 using the following functions.
661 __isl_give isl_local_space *isl_basic_set_get_local_space(
662 __isl_keep isl_basic_set *bset);
665 __isl_give isl_local_space *isl_basic_map_get_local_space(
666 __isl_keep isl_basic_map *bmap);
668 A new local space can be created from a space using
670 #include <isl/local_space.h>
671 __isl_give isl_local_space *isl_local_space_from_space(
672 __isl_take isl_space *space);
674 They can be inspected, copied and freed using the following functions.
676 #include <isl/local_space.h>
677 isl_ctx *isl_local_space_get_ctx(
678 __isl_keep isl_local_space *ls);
679 int isl_local_space_dim(__isl_keep isl_local_space *ls,
680 enum isl_dim_type type);
681 const char *isl_local_space_get_dim_name(
682 __isl_keep isl_local_space *ls,
683 enum isl_dim_type type, unsigned pos);
684 __isl_give isl_local_space *isl_local_space_set_dim_name(
685 __isl_take isl_local_space *ls,
686 enum isl_dim_type type, unsigned pos, const char *s);
687 __isl_give isl_space *isl_local_space_get_space(
688 __isl_keep isl_local_space *ls);
689 __isl_give isl_div *isl_local_space_get_div(
690 __isl_keep isl_local_space *ls, int pos);
691 __isl_give isl_local_space *isl_local_space_copy(
692 __isl_keep isl_local_space *ls);
693 void *isl_local_space_free(__isl_take isl_local_space *ls);
695 Two local spaces can be compared using
697 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
698 __isl_keep isl_local_space *ls2);
700 Local spaces can be created from other local spaces
701 using the following functions.
703 __isl_give isl_local_space *isl_local_space_from_domain(
704 __isl_take isl_local_space *ls);
705 __isl_give isl_local_space *isl_local_space_add_dims(
706 __isl_take isl_local_space *ls,
707 enum isl_dim_type type, unsigned n);
708 __isl_give isl_local_space *isl_local_space_insert_dims(
709 __isl_take isl_local_space *ls,
710 enum isl_dim_type type, unsigned first, unsigned n);
711 __isl_give isl_local_space *isl_local_space_drop_dims(
712 __isl_take isl_local_space *ls,
713 enum isl_dim_type type, unsigned first, unsigned n);
715 =head2 Input and Output
717 C<isl> supports its own input/output format, which is similar
718 to the C<Omega> format, but also supports the C<PolyLib> format
723 The C<isl> format is similar to that of C<Omega>, but has a different
724 syntax for describing the parameters and allows for the definition
725 of an existentially quantified variable as the integer division
726 of an affine expression.
727 For example, the set of integers C<i> between C<0> and C<n>
728 such that C<i % 10 <= 6> can be described as
730 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
733 A set or relation can have several disjuncts, separated
734 by the keyword C<or>. Each disjunct is either a conjunction
735 of constraints or a projection (C<exists>) of a conjunction
736 of constraints. The constraints are separated by the keyword
739 =head3 C<PolyLib> format
741 If the represented set is a union, then the first line
742 contains a single number representing the number of disjuncts.
743 Otherwise, a line containing the number C<1> is optional.
745 Each disjunct is represented by a matrix of constraints.
746 The first line contains two numbers representing
747 the number of rows and columns,
748 where the number of rows is equal to the number of constraints
749 and the number of columns is equal to two plus the number of variables.
750 The following lines contain the actual rows of the constraint matrix.
751 In each row, the first column indicates whether the constraint
752 is an equality (C<0>) or inequality (C<1>). The final column
753 corresponds to the constant term.
755 If the set is parametric, then the coefficients of the parameters
756 appear in the last columns before the constant column.
757 The coefficients of any existentially quantified variables appear
758 between those of the set variables and those of the parameters.
760 =head3 Extended C<PolyLib> format
762 The extended C<PolyLib> format is nearly identical to the
763 C<PolyLib> format. The only difference is that the line
764 containing the number of rows and columns of a constraint matrix
765 also contains four additional numbers:
766 the number of output dimensions, the number of input dimensions,
767 the number of local dimensions (i.e., the number of existentially
768 quantified variables) and the number of parameters.
769 For sets, the number of ``output'' dimensions is equal
770 to the number of set dimensions, while the number of ``input''
776 __isl_give isl_basic_set *isl_basic_set_read_from_file(
777 isl_ctx *ctx, FILE *input, int nparam);
778 __isl_give isl_basic_set *isl_basic_set_read_from_str(
779 isl_ctx *ctx, const char *str, int nparam);
780 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
781 FILE *input, int nparam);
782 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
783 const char *str, int nparam);
786 __isl_give isl_basic_map *isl_basic_map_read_from_file(
787 isl_ctx *ctx, FILE *input, int nparam);
788 __isl_give isl_basic_map *isl_basic_map_read_from_str(
789 isl_ctx *ctx, const char *str, int nparam);
790 __isl_give isl_map *isl_map_read_from_file(
791 isl_ctx *ctx, FILE *input, int nparam);
792 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
793 const char *str, int nparam);
795 #include <isl/union_set.h>
796 __isl_give isl_union_set *isl_union_set_read_from_file(
797 isl_ctx *ctx, FILE *input);
798 __isl_give isl_union_set *isl_union_set_read_from_str(
799 isl_ctx *ctx, const char *str);
801 #include <isl/union_map.h>
802 __isl_give isl_union_map *isl_union_map_read_from_file(
803 isl_ctx *ctx, FILE *input);
804 __isl_give isl_union_map *isl_union_map_read_from_str(
805 isl_ctx *ctx, const char *str);
807 The input format is autodetected and may be either the C<PolyLib> format
808 or the C<isl> format.
809 C<nparam> specifies how many of the final columns in
810 the C<PolyLib> format correspond to parameters.
811 If input is given in the C<isl> format, then the number
812 of parameters needs to be equal to C<nparam>.
813 If C<nparam> is negative, then any number of parameters
814 is accepted in the C<isl> format and zero parameters
815 are assumed in the C<PolyLib> format.
819 Before anything can be printed, an C<isl_printer> needs to
822 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
824 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
825 void isl_printer_free(__isl_take isl_printer *printer);
826 __isl_give char *isl_printer_get_str(
827 __isl_keep isl_printer *printer);
829 The behavior of the printer can be modified in various ways
831 __isl_give isl_printer *isl_printer_set_output_format(
832 __isl_take isl_printer *p, int output_format);
833 __isl_give isl_printer *isl_printer_set_indent(
834 __isl_take isl_printer *p, int indent);
835 __isl_give isl_printer *isl_printer_indent(
836 __isl_take isl_printer *p, int indent);
837 __isl_give isl_printer *isl_printer_set_prefix(
838 __isl_take isl_printer *p, const char *prefix);
839 __isl_give isl_printer *isl_printer_set_suffix(
840 __isl_take isl_printer *p, const char *suffix);
842 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
843 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
844 and defaults to C<ISL_FORMAT_ISL>.
845 Each line in the output is indented by C<indent> (set by
846 C<isl_printer_set_indent>) spaces
847 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
848 In the C<PolyLib> format output,
849 the coefficients of the existentially quantified variables
850 appear between those of the set variables and those
852 The function C<isl_printer_indent> increases the indentation
853 by the specified amount (which may be negative).
855 To actually print something, use
858 __isl_give isl_printer *isl_printer_print_basic_set(
859 __isl_take isl_printer *printer,
860 __isl_keep isl_basic_set *bset);
861 __isl_give isl_printer *isl_printer_print_set(
862 __isl_take isl_printer *printer,
863 __isl_keep isl_set *set);
866 __isl_give isl_printer *isl_printer_print_basic_map(
867 __isl_take isl_printer *printer,
868 __isl_keep isl_basic_map *bmap);
869 __isl_give isl_printer *isl_printer_print_map(
870 __isl_take isl_printer *printer,
871 __isl_keep isl_map *map);
873 #include <isl/union_set.h>
874 __isl_give isl_printer *isl_printer_print_union_set(
875 __isl_take isl_printer *p,
876 __isl_keep isl_union_set *uset);
878 #include <isl/union_map.h>
879 __isl_give isl_printer *isl_printer_print_union_map(
880 __isl_take isl_printer *p,
881 __isl_keep isl_union_map *umap);
883 When called on a file printer, the following function flushes
884 the file. When called on a string printer, the buffer is cleared.
886 __isl_give isl_printer *isl_printer_flush(
887 __isl_take isl_printer *p);
889 =head2 Creating New Sets and Relations
891 C<isl> has functions for creating some standard sets and relations.
895 =item * Empty sets and relations
897 __isl_give isl_basic_set *isl_basic_set_empty(
898 __isl_take isl_space *space);
899 __isl_give isl_basic_map *isl_basic_map_empty(
900 __isl_take isl_space *space);
901 __isl_give isl_set *isl_set_empty(
902 __isl_take isl_space *space);
903 __isl_give isl_map *isl_map_empty(
904 __isl_take isl_space *space);
905 __isl_give isl_union_set *isl_union_set_empty(
906 __isl_take isl_space *space);
907 __isl_give isl_union_map *isl_union_map_empty(
908 __isl_take isl_space *space);
910 For C<isl_union_set>s and C<isl_union_map>s, the space
911 is only used to specify the parameters.
913 =item * Universe sets and relations
915 __isl_give isl_basic_set *isl_basic_set_universe(
916 __isl_take isl_space *space);
917 __isl_give isl_basic_map *isl_basic_map_universe(
918 __isl_take isl_space *space);
919 __isl_give isl_set *isl_set_universe(
920 __isl_take isl_space *space);
921 __isl_give isl_map *isl_map_universe(
922 __isl_take isl_space *space);
923 __isl_give isl_union_set *isl_union_set_universe(
924 __isl_take isl_union_set *uset);
925 __isl_give isl_union_map *isl_union_map_universe(
926 __isl_take isl_union_map *umap);
928 The sets and relations constructed by the functions above
929 contain all integer values, while those constructed by the
930 functions below only contain non-negative values.
932 __isl_give isl_basic_set *isl_basic_set_nat_universe(
933 __isl_take isl_space *space);
934 __isl_give isl_basic_map *isl_basic_map_nat_universe(
935 __isl_take isl_space *space);
936 __isl_give isl_set *isl_set_nat_universe(
937 __isl_take isl_space *space);
938 __isl_give isl_map *isl_map_nat_universe(
939 __isl_take isl_space *space);
941 =item * Identity relations
943 __isl_give isl_basic_map *isl_basic_map_identity(
944 __isl_take isl_space *space);
945 __isl_give isl_map *isl_map_identity(
946 __isl_take isl_space *space);
948 The number of input and output dimensions in C<space> needs
951 =item * Lexicographic order
953 __isl_give isl_map *isl_map_lex_lt(
954 __isl_take isl_space *set_space);
955 __isl_give isl_map *isl_map_lex_le(
956 __isl_take isl_space *set_space);
957 __isl_give isl_map *isl_map_lex_gt(
958 __isl_take isl_space *set_space);
959 __isl_give isl_map *isl_map_lex_ge(
960 __isl_take isl_space *set_space);
961 __isl_give isl_map *isl_map_lex_lt_first(
962 __isl_take isl_space *space, unsigned n);
963 __isl_give isl_map *isl_map_lex_le_first(
964 __isl_take isl_space *space, unsigned n);
965 __isl_give isl_map *isl_map_lex_gt_first(
966 __isl_take isl_space *space, unsigned n);
967 __isl_give isl_map *isl_map_lex_ge_first(
968 __isl_take isl_space *space, unsigned n);
970 The first four functions take a space for a B<set>
971 and return relations that express that the elements in the domain
972 are lexicographically less
973 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
974 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
975 than the elements in the range.
976 The last four functions take a space for a map
977 and return relations that express that the first C<n> dimensions
978 in the domain are lexicographically less
979 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
980 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
981 than the first C<n> dimensions in the range.
985 A basic set or relation can be converted to a set or relation
986 using the following functions.
988 __isl_give isl_set *isl_set_from_basic_set(
989 __isl_take isl_basic_set *bset);
990 __isl_give isl_map *isl_map_from_basic_map(
991 __isl_take isl_basic_map *bmap);
993 Sets and relations can be converted to union sets and relations
994 using the following functions.
996 __isl_give isl_union_map *isl_union_map_from_map(
997 __isl_take isl_map *map);
998 __isl_give isl_union_set *isl_union_set_from_set(
999 __isl_take isl_set *set);
1001 The inverse conversions below can only be used if the input
1002 union set or relation is known to contain elements in exactly one
1005 __isl_give isl_set *isl_set_from_union_set(
1006 __isl_take isl_union_set *uset);
1007 __isl_give isl_map *isl_map_from_union_map(
1008 __isl_take isl_union_map *umap);
1010 Sets and relations can be copied and freed again using the following
1013 __isl_give isl_basic_set *isl_basic_set_copy(
1014 __isl_keep isl_basic_set *bset);
1015 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1016 __isl_give isl_union_set *isl_union_set_copy(
1017 __isl_keep isl_union_set *uset);
1018 __isl_give isl_basic_map *isl_basic_map_copy(
1019 __isl_keep isl_basic_map *bmap);
1020 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1021 __isl_give isl_union_map *isl_union_map_copy(
1022 __isl_keep isl_union_map *umap);
1023 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1024 void isl_set_free(__isl_take isl_set *set);
1025 void *isl_union_set_free(__isl_take isl_union_set *uset);
1026 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1027 void isl_map_free(__isl_take isl_map *map);
1028 void *isl_union_map_free(__isl_take isl_union_map *umap);
1030 Other sets and relations can be constructed by starting
1031 from a universe set or relation, adding equality and/or
1032 inequality constraints and then projecting out the
1033 existentially quantified variables, if any.
1034 Constraints can be constructed, manipulated and
1035 added to (or removed from) (basic) sets and relations
1036 using the following functions.
1038 #include <isl/constraint.h>
1039 __isl_give isl_constraint *isl_equality_alloc(
1040 __isl_take isl_space *space);
1041 __isl_give isl_constraint *isl_inequality_alloc(
1042 __isl_take isl_space *space);
1043 __isl_give isl_constraint *isl_constraint_set_constant(
1044 __isl_take isl_constraint *constraint, isl_int v);
1045 __isl_give isl_constraint *isl_constraint_set_constant_si(
1046 __isl_take isl_constraint *constraint, int v);
1047 __isl_give isl_constraint *isl_constraint_set_coefficient(
1048 __isl_take isl_constraint *constraint,
1049 enum isl_dim_type type, int pos, isl_int v);
1050 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1051 __isl_take isl_constraint *constraint,
1052 enum isl_dim_type type, int pos, int v);
1053 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1054 __isl_take isl_basic_map *bmap,
1055 __isl_take isl_constraint *constraint);
1056 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1057 __isl_take isl_basic_set *bset,
1058 __isl_take isl_constraint *constraint);
1059 __isl_give isl_map *isl_map_add_constraint(
1060 __isl_take isl_map *map,
1061 __isl_take isl_constraint *constraint);
1062 __isl_give isl_set *isl_set_add_constraint(
1063 __isl_take isl_set *set,
1064 __isl_take isl_constraint *constraint);
1065 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1066 __isl_take isl_basic_set *bset,
1067 __isl_take isl_constraint *constraint);
1069 For example, to create a set containing the even integers
1070 between 10 and 42, you would use the following code.
1075 isl_basic_set *bset;
1078 space = isl_space_set_alloc(ctx, 0, 2);
1079 bset = isl_basic_set_universe(isl_space_copy(space));
1081 c = isl_equality_alloc(isl_space_copy(space));
1082 isl_int_set_si(v, -1);
1083 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1084 isl_int_set_si(v, 2);
1085 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1086 bset = isl_basic_set_add_constraint(bset, c);
1088 c = isl_inequality_alloc(isl_space_copy(space));
1089 isl_int_set_si(v, -10);
1090 isl_constraint_set_constant(c, v);
1091 isl_int_set_si(v, 1);
1092 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1093 bset = isl_basic_set_add_constraint(bset, c);
1095 c = isl_inequality_alloc(space);
1096 isl_int_set_si(v, 42);
1097 isl_constraint_set_constant(c, v);
1098 isl_int_set_si(v, -1);
1099 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1100 bset = isl_basic_set_add_constraint(bset, c);
1102 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1108 isl_basic_set *bset;
1109 bset = isl_basic_set_read_from_str(ctx,
1110 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1112 A basic set or relation can also be constructed from two matrices
1113 describing the equalities and the inequalities.
1115 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1116 __isl_take isl_space *space,
1117 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1118 enum isl_dim_type c1,
1119 enum isl_dim_type c2, enum isl_dim_type c3,
1120 enum isl_dim_type c4);
1121 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1122 __isl_take isl_space *space,
1123 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1124 enum isl_dim_type c1,
1125 enum isl_dim_type c2, enum isl_dim_type c3,
1126 enum isl_dim_type c4, enum isl_dim_type c5);
1128 The C<isl_dim_type> arguments indicate the order in which
1129 different kinds of variables appear in the input matrices
1130 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1131 C<isl_dim_set> and C<isl_dim_div> for sets and
1132 of C<isl_dim_cst>, C<isl_dim_param>,
1133 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1135 A (basic) set or relation can also be constructed from a (piecewise)
1137 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1139 __isl_give isl_basic_map *isl_basic_map_from_aff(
1140 __isl_take isl_aff *aff);
1141 __isl_give isl_set *isl_set_from_pw_aff(
1142 __isl_take isl_pw_aff *pwaff);
1143 __isl_give isl_map *isl_map_from_pw_aff(
1144 __isl_take isl_pw_aff *pwaff);
1145 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1146 __isl_take isl_space *domain_space,
1147 __isl_take isl_aff_list *list);
1149 The C<domain_dim> argument describes the domain of the resulting
1150 basic relation. It is required because the C<list> may consist
1151 of zero affine expressions.
1153 =head2 Inspecting Sets and Relations
1155 Usually, the user should not have to care about the actual constraints
1156 of the sets and maps, but should instead apply the abstract operations
1157 explained in the following sections.
1158 Occasionally, however, it may be required to inspect the individual
1159 coefficients of the constraints. This section explains how to do so.
1160 In these cases, it may also be useful to have C<isl> compute
1161 an explicit representation of the existentially quantified variables.
1163 __isl_give isl_set *isl_set_compute_divs(
1164 __isl_take isl_set *set);
1165 __isl_give isl_map *isl_map_compute_divs(
1166 __isl_take isl_map *map);
1167 __isl_give isl_union_set *isl_union_set_compute_divs(
1168 __isl_take isl_union_set *uset);
1169 __isl_give isl_union_map *isl_union_map_compute_divs(
1170 __isl_take isl_union_map *umap);
1172 This explicit representation defines the existentially quantified
1173 variables as integer divisions of the other variables, possibly
1174 including earlier existentially quantified variables.
1175 An explicitly represented existentially quantified variable therefore
1176 has a unique value when the values of the other variables are known.
1177 If, furthermore, the same existentials, i.e., existentials
1178 with the same explicit representations, should appear in the
1179 same order in each of the disjuncts of a set or map, then the user should call
1180 either of the following functions.
1182 __isl_give isl_set *isl_set_align_divs(
1183 __isl_take isl_set *set);
1184 __isl_give isl_map *isl_map_align_divs(
1185 __isl_take isl_map *map);
1187 Alternatively, the existentially quantified variables can be removed
1188 using the following functions, which compute an overapproximation.
1190 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1191 __isl_take isl_basic_set *bset);
1192 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1193 __isl_take isl_basic_map *bmap);
1194 __isl_give isl_set *isl_set_remove_divs(
1195 __isl_take isl_set *set);
1196 __isl_give isl_map *isl_map_remove_divs(
1197 __isl_take isl_map *map);
1199 To iterate over all the sets or maps in a union set or map, use
1201 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1202 int (*fn)(__isl_take isl_set *set, void *user),
1204 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1205 int (*fn)(__isl_take isl_map *map, void *user),
1208 The number of sets or maps in a union set or map can be obtained
1211 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1212 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1214 To extract the set or map in a given space from a union, use
1216 __isl_give isl_set *isl_union_set_extract_set(
1217 __isl_keep isl_union_set *uset,
1218 __isl_take isl_space *space);
1219 __isl_give isl_map *isl_union_map_extract_map(
1220 __isl_keep isl_union_map *umap,
1221 __isl_take isl_space *space);
1223 To iterate over all the basic sets or maps in a set or map, use
1225 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1226 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1228 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1229 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1232 The callback function C<fn> should return 0 if successful and
1233 -1 if an error occurs. In the latter case, or if any other error
1234 occurs, the above functions will return -1.
1236 It should be noted that C<isl> does not guarantee that
1237 the basic sets or maps passed to C<fn> are disjoint.
1238 If this is required, then the user should call one of
1239 the following functions first.
1241 __isl_give isl_set *isl_set_make_disjoint(
1242 __isl_take isl_set *set);
1243 __isl_give isl_map *isl_map_make_disjoint(
1244 __isl_take isl_map *map);
1246 The number of basic sets in a set can be obtained
1249 int isl_set_n_basic_set(__isl_keep isl_set *set);
1251 To iterate over the constraints of a basic set or map, use
1253 #include <isl/constraint.h>
1255 int isl_basic_map_foreach_constraint(
1256 __isl_keep isl_basic_map *bmap,
1257 int (*fn)(__isl_take isl_constraint *c, void *user),
1259 void *isl_constraint_free(__isl_take isl_constraint *c);
1261 Again, the callback function C<fn> should return 0 if successful and
1262 -1 if an error occurs. In the latter case, or if any other error
1263 occurs, the above functions will return -1.
1264 The constraint C<c> represents either an equality or an inequality.
1265 Use the following function to find out whether a constraint
1266 represents an equality. If not, it represents an inequality.
1268 int isl_constraint_is_equality(
1269 __isl_keep isl_constraint *constraint);
1271 The coefficients of the constraints can be inspected using
1272 the following functions.
1274 void isl_constraint_get_constant(
1275 __isl_keep isl_constraint *constraint, isl_int *v);
1276 void isl_constraint_get_coefficient(
1277 __isl_keep isl_constraint *constraint,
1278 enum isl_dim_type type, int pos, isl_int *v);
1279 int isl_constraint_involves_dims(
1280 __isl_keep isl_constraint *constraint,
1281 enum isl_dim_type type, unsigned first, unsigned n);
1283 The explicit representations of the existentially quantified
1284 variables can be inspected using the following functions.
1285 Note that the user is only allowed to use these functions
1286 if the inspected set or map is the result of a call
1287 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1289 __isl_give isl_div *isl_constraint_div(
1290 __isl_keep isl_constraint *constraint, int pos);
1291 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1292 void isl_div_get_constant(__isl_keep isl_div *div,
1294 void isl_div_get_denominator(__isl_keep isl_div *div,
1296 void isl_div_get_coefficient(__isl_keep isl_div *div,
1297 enum isl_dim_type type, int pos, isl_int *v);
1299 To obtain the constraints of a basic set or map in matrix
1300 form, use the following functions.
1302 __isl_give isl_mat *isl_basic_set_equalities_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_set_inequalities_matrix(
1307 __isl_keep isl_basic_set *bset,
1308 enum isl_dim_type c1, enum isl_dim_type c2,
1309 enum isl_dim_type c3, enum isl_dim_type c4);
1310 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1311 __isl_keep isl_basic_map *bmap,
1312 enum isl_dim_type c1,
1313 enum isl_dim_type c2, enum isl_dim_type c3,
1314 enum isl_dim_type c4, enum isl_dim_type c5);
1315 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1316 __isl_keep isl_basic_map *bmap,
1317 enum isl_dim_type c1,
1318 enum isl_dim_type c2, enum isl_dim_type c3,
1319 enum isl_dim_type c4, enum isl_dim_type c5);
1321 The C<isl_dim_type> arguments dictate the order in which
1322 different kinds of variables appear in the resulting matrix
1323 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1324 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1326 The number of parameters, input, output or set dimensions can
1327 be obtained using the following functions.
1329 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1330 enum isl_dim_type type);
1331 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1332 enum isl_dim_type type);
1333 unsigned isl_set_dim(__isl_keep isl_set *set,
1334 enum isl_dim_type type);
1335 unsigned isl_map_dim(__isl_keep isl_map *map,
1336 enum isl_dim_type type);
1338 To check whether the description of a set or relation depends
1339 on one or more given dimensions, it is not necessary to iterate over all
1340 constraints. Instead the following functions can be used.
1342 int isl_basic_set_involves_dims(
1343 __isl_keep isl_basic_set *bset,
1344 enum isl_dim_type type, unsigned first, unsigned n);
1345 int isl_set_involves_dims(__isl_keep isl_set *set,
1346 enum isl_dim_type type, unsigned first, unsigned n);
1347 int isl_basic_map_involves_dims(
1348 __isl_keep isl_basic_map *bmap,
1349 enum isl_dim_type type, unsigned first, unsigned n);
1350 int isl_map_involves_dims(__isl_keep isl_map *map,
1351 enum isl_dim_type type, unsigned first, unsigned n);
1353 Similarly, the following functions can be used to check whether
1354 a given dimension is involved in any lower or upper bound.
1356 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1357 enum isl_dim_type type, unsigned pos);
1358 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1359 enum isl_dim_type type, unsigned pos);
1361 The identifiers or names of the domain and range spaces of a set
1362 or relation can be read off or set using the following functions.
1364 __isl_give isl_set *isl_set_set_tuple_id(
1365 __isl_take isl_set *set, __isl_take isl_id *id);
1366 __isl_give isl_set *isl_set_reset_tuple_id(
1367 __isl_take isl_set *set);
1368 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1369 __isl_give isl_id *isl_set_get_tuple_id(
1370 __isl_keep isl_set *set);
1371 __isl_give isl_map *isl_map_set_tuple_id(
1372 __isl_take isl_map *map, enum isl_dim_type type,
1373 __isl_take isl_id *id);
1374 __isl_give isl_map *isl_map_reset_tuple_id(
1375 __isl_take isl_map *map, enum isl_dim_type type);
1376 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1377 enum isl_dim_type type);
1378 __isl_give isl_id *isl_map_get_tuple_id(
1379 __isl_keep isl_map *map, enum isl_dim_type type);
1381 const char *isl_basic_set_get_tuple_name(
1382 __isl_keep isl_basic_set *bset);
1383 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1384 __isl_take isl_basic_set *set, const char *s);
1385 const char *isl_set_get_tuple_name(
1386 __isl_keep isl_set *set);
1387 const char *isl_basic_map_get_tuple_name(
1388 __isl_keep isl_basic_map *bmap,
1389 enum isl_dim_type type);
1390 const char *isl_map_get_tuple_name(
1391 __isl_keep isl_map *map,
1392 enum isl_dim_type type);
1394 As with C<isl_space_get_tuple_name>, the value returned points to
1395 an internal data structure.
1396 The identifiers, positions or names of individual dimensions can be
1397 read off using the following functions.
1399 __isl_give isl_set *isl_set_set_dim_id(
1400 __isl_take isl_set *set, enum isl_dim_type type,
1401 unsigned pos, __isl_take isl_id *id);
1402 int isl_set_has_dim_id(__isl_keep isl_set *set,
1403 enum isl_dim_type type, unsigned pos);
1404 __isl_give isl_id *isl_set_get_dim_id(
1405 __isl_keep isl_set *set, enum isl_dim_type type,
1407 __isl_give isl_map *isl_map_set_dim_id(
1408 __isl_take isl_map *map, enum isl_dim_type type,
1409 unsigned pos, __isl_take isl_id *id);
1410 int isl_map_has_dim_id(__isl_keep isl_map *map,
1411 enum isl_dim_type type, unsigned pos);
1412 __isl_give isl_id *isl_map_get_dim_id(
1413 __isl_keep isl_map *map, enum isl_dim_type type,
1416 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1417 enum isl_dim_type type, __isl_keep isl_id *id);
1418 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1419 enum isl_dim_type type, __isl_keep isl_id *id);
1421 const char *isl_constraint_get_dim_name(
1422 __isl_keep isl_constraint *constraint,
1423 enum isl_dim_type type, unsigned pos);
1424 const char *isl_basic_set_get_dim_name(
1425 __isl_keep isl_basic_set *bset,
1426 enum isl_dim_type type, unsigned pos);
1427 const char *isl_set_get_dim_name(
1428 __isl_keep isl_set *set,
1429 enum isl_dim_type type, unsigned pos);
1430 const char *isl_basic_map_get_dim_name(
1431 __isl_keep isl_basic_map *bmap,
1432 enum isl_dim_type type, unsigned pos);
1433 const char *isl_map_get_dim_name(
1434 __isl_keep isl_map *map,
1435 enum isl_dim_type type, unsigned pos);
1437 These functions are mostly useful to obtain the identifiers, positions
1438 or names of the parameters. Identifiers of individual dimensions are
1439 essentially only useful for printing. They are ignored by all other
1440 operations and may not be preserved across those operations.
1444 =head3 Unary Properties
1450 The following functions test whether the given set or relation
1451 contains any integer points. The ``plain'' variants do not perform
1452 any computations, but simply check if the given set or relation
1453 is already known to be empty.
1455 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1456 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1457 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1458 int isl_set_is_empty(__isl_keep isl_set *set);
1459 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1460 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1461 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1462 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1463 int isl_map_is_empty(__isl_keep isl_map *map);
1464 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1466 =item * Universality
1468 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1469 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1470 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1472 =item * Single-valuedness
1474 int isl_map_is_single_valued(__isl_keep isl_map *map);
1475 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1479 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1480 int isl_map_is_injective(__isl_keep isl_map *map);
1481 int isl_union_map_plain_is_injective(
1482 __isl_keep isl_union_map *umap);
1483 int isl_union_map_is_injective(
1484 __isl_keep isl_union_map *umap);
1488 int isl_map_is_bijective(__isl_keep isl_map *map);
1489 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1493 int isl_basic_map_plain_is_fixed(
1494 __isl_keep isl_basic_map *bmap,
1495 enum isl_dim_type type, unsigned pos,
1497 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1498 enum isl_dim_type type, unsigned pos,
1501 Check if the relation obviously lies on a hyperplane where the given dimension
1502 has a fixed value and if so, return that value in C<*val>.
1506 The following functions check whether the domain of the given
1507 (basic) set is a wrapped relation.
1509 int isl_basic_set_is_wrapping(
1510 __isl_keep isl_basic_set *bset);
1511 int isl_set_is_wrapping(__isl_keep isl_set *set);
1513 =item * Internal Product
1515 int isl_basic_map_can_zip(
1516 __isl_keep isl_basic_map *bmap);
1517 int isl_map_can_zip(__isl_keep isl_map *map);
1519 Check whether the product of domain and range of the given relation
1521 i.e., whether both domain and range are nested relations.
1525 =head3 Binary Properties
1531 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1532 __isl_keep isl_set *set2);
1533 int isl_set_is_equal(__isl_keep isl_set *set1,
1534 __isl_keep isl_set *set2);
1535 int isl_union_set_is_equal(
1536 __isl_keep isl_union_set *uset1,
1537 __isl_keep isl_union_set *uset2);
1538 int isl_basic_map_is_equal(
1539 __isl_keep isl_basic_map *bmap1,
1540 __isl_keep isl_basic_map *bmap2);
1541 int isl_map_is_equal(__isl_keep isl_map *map1,
1542 __isl_keep isl_map *map2);
1543 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1544 __isl_keep isl_map *map2);
1545 int isl_union_map_is_equal(
1546 __isl_keep isl_union_map *umap1,
1547 __isl_keep isl_union_map *umap2);
1549 =item * Disjointness
1551 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1552 __isl_keep isl_set *set2);
1556 int isl_set_is_subset(__isl_keep isl_set *set1,
1557 __isl_keep isl_set *set2);
1558 int isl_set_is_strict_subset(
1559 __isl_keep isl_set *set1,
1560 __isl_keep isl_set *set2);
1561 int isl_union_set_is_subset(
1562 __isl_keep isl_union_set *uset1,
1563 __isl_keep isl_union_set *uset2);
1564 int isl_union_set_is_strict_subset(
1565 __isl_keep isl_union_set *uset1,
1566 __isl_keep isl_union_set *uset2);
1567 int isl_basic_map_is_subset(
1568 __isl_keep isl_basic_map *bmap1,
1569 __isl_keep isl_basic_map *bmap2);
1570 int isl_basic_map_is_strict_subset(
1571 __isl_keep isl_basic_map *bmap1,
1572 __isl_keep isl_basic_map *bmap2);
1573 int isl_map_is_subset(
1574 __isl_keep isl_map *map1,
1575 __isl_keep isl_map *map2);
1576 int isl_map_is_strict_subset(
1577 __isl_keep isl_map *map1,
1578 __isl_keep isl_map *map2);
1579 int isl_union_map_is_subset(
1580 __isl_keep isl_union_map *umap1,
1581 __isl_keep isl_union_map *umap2);
1582 int isl_union_map_is_strict_subset(
1583 __isl_keep isl_union_map *umap1,
1584 __isl_keep isl_union_map *umap2);
1588 =head2 Unary Operations
1594 __isl_give isl_set *isl_set_complement(
1595 __isl_take isl_set *set);
1599 __isl_give isl_basic_map *isl_basic_map_reverse(
1600 __isl_take isl_basic_map *bmap);
1601 __isl_give isl_map *isl_map_reverse(
1602 __isl_take isl_map *map);
1603 __isl_give isl_union_map *isl_union_map_reverse(
1604 __isl_take isl_union_map *umap);
1608 __isl_give isl_basic_set *isl_basic_set_project_out(
1609 __isl_take isl_basic_set *bset,
1610 enum isl_dim_type type, unsigned first, unsigned n);
1611 __isl_give isl_basic_map *isl_basic_map_project_out(
1612 __isl_take isl_basic_map *bmap,
1613 enum isl_dim_type type, unsigned first, unsigned n);
1614 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1615 enum isl_dim_type type, unsigned first, unsigned n);
1616 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1617 enum isl_dim_type type, unsigned first, unsigned n);
1618 __isl_give isl_basic_set *isl_basic_map_domain(
1619 __isl_take isl_basic_map *bmap);
1620 __isl_give isl_basic_set *isl_basic_map_range(
1621 __isl_take isl_basic_map *bmap);
1622 __isl_give isl_set *isl_map_domain(
1623 __isl_take isl_map *bmap);
1624 __isl_give isl_set *isl_map_range(
1625 __isl_take isl_map *map);
1626 __isl_give isl_union_set *isl_union_map_domain(
1627 __isl_take isl_union_map *umap);
1628 __isl_give isl_union_set *isl_union_map_range(
1629 __isl_take isl_union_map *umap);
1631 __isl_give isl_basic_map *isl_basic_map_domain_map(
1632 __isl_take isl_basic_map *bmap);
1633 __isl_give isl_basic_map *isl_basic_map_range_map(
1634 __isl_take isl_basic_map *bmap);
1635 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1636 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1637 __isl_give isl_union_map *isl_union_map_domain_map(
1638 __isl_take isl_union_map *umap);
1639 __isl_give isl_union_map *isl_union_map_range_map(
1640 __isl_take isl_union_map *umap);
1642 The functions above construct a (basic, regular or union) relation
1643 that maps (a wrapped version of) the input relation to its domain or range.
1647 __isl_give isl_set *isl_set_eliminate(
1648 __isl_take isl_set *set, enum isl_dim_type type,
1649 unsigned first, unsigned n);
1651 Eliminate the coefficients for the given dimensions from the constraints,
1652 without removing the dimensions.
1656 __isl_give isl_basic_set *isl_basic_set_fix(
1657 __isl_take isl_basic_set *bset,
1658 enum isl_dim_type type, unsigned pos,
1660 __isl_give isl_basic_set *isl_basic_set_fix_si(
1661 __isl_take isl_basic_set *bset,
1662 enum isl_dim_type type, unsigned pos, int value);
1663 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1664 enum isl_dim_type type, unsigned pos,
1666 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1667 enum isl_dim_type type, unsigned pos, int value);
1668 __isl_give isl_basic_map *isl_basic_map_fix_si(
1669 __isl_take isl_basic_map *bmap,
1670 enum isl_dim_type type, unsigned pos, int value);
1671 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1672 enum isl_dim_type type, unsigned pos, int value);
1674 Intersect the set or relation with the hyperplane where the given
1675 dimension has the fixed given value.
1677 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1678 enum isl_dim_type type1, int pos1,
1679 enum isl_dim_type type2, int pos2);
1680 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1681 enum isl_dim_type type1, int pos1,
1682 enum isl_dim_type type2, int pos2);
1684 Intersect the set or relation with the hyperplane where the given
1685 dimensions are equal to each other.
1687 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1688 enum isl_dim_type type1, int pos1,
1689 enum isl_dim_type type2, int pos2);
1691 Intersect the relation with the hyperplane where the given
1692 dimensions have opposite values.
1696 __isl_give isl_map *isl_set_identity(
1697 __isl_take isl_set *set);
1698 __isl_give isl_union_map *isl_union_set_identity(
1699 __isl_take isl_union_set *uset);
1701 Construct an identity relation on the given (union) set.
1705 __isl_give isl_basic_set *isl_basic_map_deltas(
1706 __isl_take isl_basic_map *bmap);
1707 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1708 __isl_give isl_union_set *isl_union_map_deltas(
1709 __isl_take isl_union_map *umap);
1711 These functions return a (basic) set containing the differences
1712 between image elements and corresponding domain elements in the input.
1714 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1715 __isl_take isl_basic_map *bmap);
1716 __isl_give isl_map *isl_map_deltas_map(
1717 __isl_take isl_map *map);
1718 __isl_give isl_union_map *isl_union_map_deltas_map(
1719 __isl_take isl_union_map *umap);
1721 The functions above construct a (basic, regular or union) relation
1722 that maps (a wrapped version of) the input relation to its delta set.
1726 Simplify the representation of a set or relation by trying
1727 to combine pairs of basic sets or relations into a single
1728 basic set or relation.
1730 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1731 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1732 __isl_give isl_union_set *isl_union_set_coalesce(
1733 __isl_take isl_union_set *uset);
1734 __isl_give isl_union_map *isl_union_map_coalesce(
1735 __isl_take isl_union_map *umap);
1737 =item * Detecting equalities
1739 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1740 __isl_take isl_basic_set *bset);
1741 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1742 __isl_take isl_basic_map *bmap);
1743 __isl_give isl_set *isl_set_detect_equalities(
1744 __isl_take isl_set *set);
1745 __isl_give isl_map *isl_map_detect_equalities(
1746 __isl_take isl_map *map);
1747 __isl_give isl_union_set *isl_union_set_detect_equalities(
1748 __isl_take isl_union_set *uset);
1749 __isl_give isl_union_map *isl_union_map_detect_equalities(
1750 __isl_take isl_union_map *umap);
1752 Simplify the representation of a set or relation by detecting implicit
1755 =item * Removing redundant constraints
1757 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1758 __isl_take isl_basic_set *bset);
1759 __isl_give isl_set *isl_set_remove_redundancies(
1760 __isl_take isl_set *set);
1761 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1762 __isl_take isl_basic_map *bmap);
1763 __isl_give isl_map *isl_map_remove_redundancies(
1764 __isl_take isl_map *map);
1768 __isl_give isl_basic_set *isl_set_convex_hull(
1769 __isl_take isl_set *set);
1770 __isl_give isl_basic_map *isl_map_convex_hull(
1771 __isl_take isl_map *map);
1773 If the input set or relation has any existentially quantified
1774 variables, then the result of these operations is currently undefined.
1778 __isl_give isl_basic_set *isl_set_simple_hull(
1779 __isl_take isl_set *set);
1780 __isl_give isl_basic_map *isl_map_simple_hull(
1781 __isl_take isl_map *map);
1782 __isl_give isl_union_map *isl_union_map_simple_hull(
1783 __isl_take isl_union_map *umap);
1785 These functions compute a single basic set or relation
1786 that contains the whole input set or relation.
1787 In particular, the output is described by translates
1788 of the constraints describing the basic sets or relations in the input.
1792 (See \autoref{s:simple hull}.)
1798 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1799 __isl_take isl_basic_set *bset);
1800 __isl_give isl_basic_set *isl_set_affine_hull(
1801 __isl_take isl_set *set);
1802 __isl_give isl_union_set *isl_union_set_affine_hull(
1803 __isl_take isl_union_set *uset);
1804 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1805 __isl_take isl_basic_map *bmap);
1806 __isl_give isl_basic_map *isl_map_affine_hull(
1807 __isl_take isl_map *map);
1808 __isl_give isl_union_map *isl_union_map_affine_hull(
1809 __isl_take isl_union_map *umap);
1811 In case of union sets and relations, the affine hull is computed
1814 =item * Polyhedral hull
1816 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1817 __isl_take isl_set *set);
1818 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1819 __isl_take isl_map *map);
1820 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1821 __isl_take isl_union_set *uset);
1822 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1823 __isl_take isl_union_map *umap);
1825 These functions compute a single basic set or relation
1826 not involving any existentially quantified variables
1827 that contains the whole input set or relation.
1828 In case of union sets and relations, the polyhedral hull is computed
1831 =item * Optimization
1833 #include <isl/ilp.h>
1834 enum isl_lp_result isl_basic_set_max(
1835 __isl_keep isl_basic_set *bset,
1836 __isl_keep isl_aff *obj, isl_int *opt)
1837 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1838 __isl_keep isl_aff *obj, isl_int *opt);
1839 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1840 __isl_keep isl_aff *obj, isl_int *opt);
1842 Compute the minimum or maximum of the integer affine expression C<obj>
1843 over the points in C<set>, returning the result in C<opt>.
1844 The return value may be one of C<isl_lp_error>,
1845 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1847 =item * Parametric optimization
1849 __isl_give isl_pw_aff *isl_set_dim_min(
1850 __isl_take isl_set *set, int pos);
1851 __isl_give isl_pw_aff *isl_set_dim_max(
1852 __isl_take isl_set *set, int pos);
1854 Compute the minimum or maximum of the given set dimension as a function of the
1855 parameters, but independently of the other set dimensions.
1856 For lexicographic optimization, see L<"Lexicographic Optimization">.
1860 The following functions compute either the set of (rational) coefficient
1861 values of valid constraints for the given set or the set of (rational)
1862 values satisfying the constraints with coefficients from the given set.
1863 Internally, these two sets of functions perform essentially the
1864 same operations, except that the set of coefficients is assumed to
1865 be a cone, while the set of values may be any polyhedron.
1866 The current implementation is based on the Farkas lemma and
1867 Fourier-Motzkin elimination, but this may change or be made optional
1868 in future. In particular, future implementations may use different
1869 dualization algorithms or skip the elimination step.
1871 __isl_give isl_basic_set *isl_basic_set_coefficients(
1872 __isl_take isl_basic_set *bset);
1873 __isl_give isl_basic_set *isl_set_coefficients(
1874 __isl_take isl_set *set);
1875 __isl_give isl_union_set *isl_union_set_coefficients(
1876 __isl_take isl_union_set *bset);
1877 __isl_give isl_basic_set *isl_basic_set_solutions(
1878 __isl_take isl_basic_set *bset);
1879 __isl_give isl_basic_set *isl_set_solutions(
1880 __isl_take isl_set *set);
1881 __isl_give isl_union_set *isl_union_set_solutions(
1882 __isl_take isl_union_set *bset);
1886 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1888 __isl_give isl_union_map *isl_union_map_power(
1889 __isl_take isl_union_map *umap, int *exact);
1891 Compute a parametric representation for all positive powers I<k> of C<map>.
1892 The result maps I<k> to a nested relation corresponding to the
1893 I<k>th power of C<map>.
1894 The result may be an overapproximation. If the result is known to be exact,
1895 then C<*exact> is set to C<1>.
1897 =item * Transitive closure
1899 __isl_give isl_map *isl_map_transitive_closure(
1900 __isl_take isl_map *map, int *exact);
1901 __isl_give isl_union_map *isl_union_map_transitive_closure(
1902 __isl_take isl_union_map *umap, int *exact);
1904 Compute the transitive closure of C<map>.
1905 The result may be an overapproximation. If the result is known to be exact,
1906 then C<*exact> is set to C<1>.
1908 =item * Reaching path lengths
1910 __isl_give isl_map *isl_map_reaching_path_lengths(
1911 __isl_take isl_map *map, int *exact);
1913 Compute a relation that maps each element in the range of C<map>
1914 to the lengths of all paths composed of edges in C<map> that
1915 end up in the given element.
1916 The result may be an overapproximation. If the result is known to be exact,
1917 then C<*exact> is set to C<1>.
1918 To compute the I<maximal> path length, the resulting relation
1919 should be postprocessed by C<isl_map_lexmax>.
1920 In particular, if the input relation is a dependence relation
1921 (mapping sources to sinks), then the maximal path length corresponds
1922 to the free schedule.
1923 Note, however, that C<isl_map_lexmax> expects the maximum to be
1924 finite, so if the path lengths are unbounded (possibly due to
1925 the overapproximation), then you will get an error message.
1929 __isl_give isl_basic_set *isl_basic_map_wrap(
1930 __isl_take isl_basic_map *bmap);
1931 __isl_give isl_set *isl_map_wrap(
1932 __isl_take isl_map *map);
1933 __isl_give isl_union_set *isl_union_map_wrap(
1934 __isl_take isl_union_map *umap);
1935 __isl_give isl_basic_map *isl_basic_set_unwrap(
1936 __isl_take isl_basic_set *bset);
1937 __isl_give isl_map *isl_set_unwrap(
1938 __isl_take isl_set *set);
1939 __isl_give isl_union_map *isl_union_set_unwrap(
1940 __isl_take isl_union_set *uset);
1944 Remove any internal structure of domain (and range) of the given
1945 set or relation. If there is any such internal structure in the input,
1946 then the name of the space is also removed.
1948 __isl_give isl_basic_set *isl_basic_set_flatten(
1949 __isl_take isl_basic_set *bset);
1950 __isl_give isl_set *isl_set_flatten(
1951 __isl_take isl_set *set);
1952 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
1953 __isl_take isl_basic_map *bmap);
1954 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1955 __isl_take isl_basic_map *bmap);
1956 __isl_give isl_map *isl_map_flatten_range(
1957 __isl_take isl_map *map);
1958 __isl_give isl_map *isl_map_flatten_domain(
1959 __isl_take isl_map *map);
1960 __isl_give isl_basic_map *isl_basic_map_flatten(
1961 __isl_take isl_basic_map *bmap);
1962 __isl_give isl_map *isl_map_flatten(
1963 __isl_take isl_map *map);
1965 __isl_give isl_map *isl_set_flatten_map(
1966 __isl_take isl_set *set);
1968 The function above constructs a relation
1969 that maps the input set to a flattened version of the set.
1973 Lift the input set to a space with extra dimensions corresponding
1974 to the existentially quantified variables in the input.
1975 In particular, the result lives in a wrapped map where the domain
1976 is the original space and the range corresponds to the original
1977 existentially quantified variables.
1979 __isl_give isl_basic_set *isl_basic_set_lift(
1980 __isl_take isl_basic_set *bset);
1981 __isl_give isl_set *isl_set_lift(
1982 __isl_take isl_set *set);
1983 __isl_give isl_union_set *isl_union_set_lift(
1984 __isl_take isl_union_set *uset);
1986 =item * Internal Product
1988 __isl_give isl_basic_map *isl_basic_map_zip(
1989 __isl_take isl_basic_map *bmap);
1990 __isl_give isl_map *isl_map_zip(
1991 __isl_take isl_map *map);
1992 __isl_give isl_union_map *isl_union_map_zip(
1993 __isl_take isl_union_map *umap);
1995 Given a relation with nested relations for domain and range,
1996 interchange the range of the domain with the domain of the range.
1998 =item * Aligning parameters
2000 __isl_give isl_set *isl_set_align_params(
2001 __isl_take isl_set *set,
2002 __isl_take isl_space *model);
2003 __isl_give isl_map *isl_map_align_params(
2004 __isl_take isl_map *map,
2005 __isl_take isl_space *model);
2007 Change the order of the parameters of the given set or relation
2008 such that the first parameters match those of C<model>.
2009 This may involve the introduction of extra parameters.
2010 All parameters need to be named.
2012 =item * Dimension manipulation
2014 __isl_give isl_set *isl_set_add_dims(
2015 __isl_take isl_set *set,
2016 enum isl_dim_type type, unsigned n);
2017 __isl_give isl_map *isl_map_add_dims(
2018 __isl_take isl_map *map,
2019 enum isl_dim_type type, unsigned n);
2020 __isl_give isl_set *isl_set_insert_dims(
2021 __isl_take isl_set *set,
2022 enum isl_dim_type type, unsigned pos, unsigned n);
2023 __isl_give isl_map *isl_map_insert_dims(
2024 __isl_take isl_map *map,
2025 enum isl_dim_type type, unsigned pos, unsigned n);
2027 It is usually not advisable to directly change the (input or output)
2028 space of a set or a relation as this removes the name and the internal
2029 structure of the space. However, the above functions can be useful
2030 to add new parameters, assuming
2031 C<isl_set_align_params> and C<isl_map_align_params>
2036 =head2 Binary Operations
2038 The two arguments of a binary operation not only need to live
2039 in the same C<isl_ctx>, they currently also need to have
2040 the same (number of) parameters.
2042 =head3 Basic Operations
2046 =item * Intersection
2048 __isl_give isl_basic_set *isl_basic_set_intersect(
2049 __isl_take isl_basic_set *bset1,
2050 __isl_take isl_basic_set *bset2);
2051 __isl_give isl_set *isl_set_intersect_params(
2052 __isl_take isl_set *set,
2053 __isl_take isl_set *params);
2054 __isl_give isl_set *isl_set_intersect(
2055 __isl_take isl_set *set1,
2056 __isl_take isl_set *set2);
2057 __isl_give isl_union_set *isl_union_set_intersect(
2058 __isl_take isl_union_set *uset1,
2059 __isl_take isl_union_set *uset2);
2060 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2061 __isl_take isl_basic_map *bmap,
2062 __isl_take isl_basic_set *bset);
2063 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2064 __isl_take isl_basic_map *bmap,
2065 __isl_take isl_basic_set *bset);
2066 __isl_give isl_basic_map *isl_basic_map_intersect(
2067 __isl_take isl_basic_map *bmap1,
2068 __isl_take isl_basic_map *bmap2);
2069 __isl_give isl_map *isl_map_intersect_params(
2070 __isl_take isl_map *map,
2071 __isl_take isl_set *params);
2072 __isl_give isl_map *isl_map_intersect_domain(
2073 __isl_take isl_map *map,
2074 __isl_take isl_set *set);
2075 __isl_give isl_map *isl_map_intersect_range(
2076 __isl_take isl_map *map,
2077 __isl_take isl_set *set);
2078 __isl_give isl_map *isl_map_intersect(
2079 __isl_take isl_map *map1,
2080 __isl_take isl_map *map2);
2081 __isl_give isl_union_map *isl_union_map_intersect_domain(
2082 __isl_take isl_union_map *umap,
2083 __isl_take isl_union_set *uset);
2084 __isl_give isl_union_map *isl_union_map_intersect_range(
2085 __isl_take isl_union_map *umap,
2086 __isl_take isl_union_set *uset);
2087 __isl_give isl_union_map *isl_union_map_intersect(
2088 __isl_take isl_union_map *umap1,
2089 __isl_take isl_union_map *umap2);
2093 __isl_give isl_set *isl_basic_set_union(
2094 __isl_take isl_basic_set *bset1,
2095 __isl_take isl_basic_set *bset2);
2096 __isl_give isl_map *isl_basic_map_union(
2097 __isl_take isl_basic_map *bmap1,
2098 __isl_take isl_basic_map *bmap2);
2099 __isl_give isl_set *isl_set_union(
2100 __isl_take isl_set *set1,
2101 __isl_take isl_set *set2);
2102 __isl_give isl_map *isl_map_union(
2103 __isl_take isl_map *map1,
2104 __isl_take isl_map *map2);
2105 __isl_give isl_union_set *isl_union_set_union(
2106 __isl_take isl_union_set *uset1,
2107 __isl_take isl_union_set *uset2);
2108 __isl_give isl_union_map *isl_union_map_union(
2109 __isl_take isl_union_map *umap1,
2110 __isl_take isl_union_map *umap2);
2112 =item * Set difference
2114 __isl_give isl_set *isl_set_subtract(
2115 __isl_take isl_set *set1,
2116 __isl_take isl_set *set2);
2117 __isl_give isl_map *isl_map_subtract(
2118 __isl_take isl_map *map1,
2119 __isl_take isl_map *map2);
2120 __isl_give isl_union_set *isl_union_set_subtract(
2121 __isl_take isl_union_set *uset1,
2122 __isl_take isl_union_set *uset2);
2123 __isl_give isl_union_map *isl_union_map_subtract(
2124 __isl_take isl_union_map *umap1,
2125 __isl_take isl_union_map *umap2);
2129 __isl_give isl_basic_set *isl_basic_set_apply(
2130 __isl_take isl_basic_set *bset,
2131 __isl_take isl_basic_map *bmap);
2132 __isl_give isl_set *isl_set_apply(
2133 __isl_take isl_set *set,
2134 __isl_take isl_map *map);
2135 __isl_give isl_union_set *isl_union_set_apply(
2136 __isl_take isl_union_set *uset,
2137 __isl_take isl_union_map *umap);
2138 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2139 __isl_take isl_basic_map *bmap1,
2140 __isl_take isl_basic_map *bmap2);
2141 __isl_give isl_basic_map *isl_basic_map_apply_range(
2142 __isl_take isl_basic_map *bmap1,
2143 __isl_take isl_basic_map *bmap2);
2144 __isl_give isl_map *isl_map_apply_domain(
2145 __isl_take isl_map *map1,
2146 __isl_take isl_map *map2);
2147 __isl_give isl_union_map *isl_union_map_apply_domain(
2148 __isl_take isl_union_map *umap1,
2149 __isl_take isl_union_map *umap2);
2150 __isl_give isl_map *isl_map_apply_range(
2151 __isl_take isl_map *map1,
2152 __isl_take isl_map *map2);
2153 __isl_give isl_union_map *isl_union_map_apply_range(
2154 __isl_take isl_union_map *umap1,
2155 __isl_take isl_union_map *umap2);
2157 =item * Cartesian Product
2159 __isl_give isl_set *isl_set_product(
2160 __isl_take isl_set *set1,
2161 __isl_take isl_set *set2);
2162 __isl_give isl_union_set *isl_union_set_product(
2163 __isl_take isl_union_set *uset1,
2164 __isl_take isl_union_set *uset2);
2165 __isl_give isl_basic_map *isl_basic_map_domain_product(
2166 __isl_take isl_basic_map *bmap1,
2167 __isl_take isl_basic_map *bmap2);
2168 __isl_give isl_basic_map *isl_basic_map_range_product(
2169 __isl_take isl_basic_map *bmap1,
2170 __isl_take isl_basic_map *bmap2);
2171 __isl_give isl_map *isl_map_domain_product(
2172 __isl_take isl_map *map1,
2173 __isl_take isl_map *map2);
2174 __isl_give isl_map *isl_map_range_product(
2175 __isl_take isl_map *map1,
2176 __isl_take isl_map *map2);
2177 __isl_give isl_union_map *isl_union_map_range_product(
2178 __isl_take isl_union_map *umap1,
2179 __isl_take isl_union_map *umap2);
2180 __isl_give isl_map *isl_map_product(
2181 __isl_take isl_map *map1,
2182 __isl_take isl_map *map2);
2183 __isl_give isl_union_map *isl_union_map_product(
2184 __isl_take isl_union_map *umap1,
2185 __isl_take isl_union_map *umap2);
2187 The above functions compute the cross product of the given
2188 sets or relations. The domains and ranges of the results
2189 are wrapped maps between domains and ranges of the inputs.
2190 To obtain a ``flat'' product, use the following functions
2193 __isl_give isl_basic_set *isl_basic_set_flat_product(
2194 __isl_take isl_basic_set *bset1,
2195 __isl_take isl_basic_set *bset2);
2196 __isl_give isl_set *isl_set_flat_product(
2197 __isl_take isl_set *set1,
2198 __isl_take isl_set *set2);
2199 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2200 __isl_take isl_basic_map *bmap1,
2201 __isl_take isl_basic_map *bmap2);
2202 __isl_give isl_map *isl_map_flat_domain_product(
2203 __isl_take isl_map *map1,
2204 __isl_take isl_map *map2);
2205 __isl_give isl_map *isl_map_flat_range_product(
2206 __isl_take isl_map *map1,
2207 __isl_take isl_map *map2);
2208 __isl_give isl_union_map *isl_union_map_flat_range_product(
2209 __isl_take isl_union_map *umap1,
2210 __isl_take isl_union_map *umap2);
2211 __isl_give isl_basic_map *isl_basic_map_flat_product(
2212 __isl_take isl_basic_map *bmap1,
2213 __isl_take isl_basic_map *bmap2);
2214 __isl_give isl_map *isl_map_flat_product(
2215 __isl_take isl_map *map1,
2216 __isl_take isl_map *map2);
2218 =item * Simplification
2220 __isl_give isl_basic_set *isl_basic_set_gist(
2221 __isl_take isl_basic_set *bset,
2222 __isl_take isl_basic_set *context);
2223 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2224 __isl_take isl_set *context);
2225 __isl_give isl_union_set *isl_union_set_gist(
2226 __isl_take isl_union_set *uset,
2227 __isl_take isl_union_set *context);
2228 __isl_give isl_basic_map *isl_basic_map_gist(
2229 __isl_take isl_basic_map *bmap,
2230 __isl_take isl_basic_map *context);
2231 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2232 __isl_take isl_map *context);
2233 __isl_give isl_union_map *isl_union_map_gist(
2234 __isl_take isl_union_map *umap,
2235 __isl_take isl_union_map *context);
2237 The gist operation returns a set or relation that has the
2238 same intersection with the context as the input set or relation.
2239 Any implicit equality in the intersection is made explicit in the result,
2240 while all inequalities that are redundant with respect to the intersection
2242 In case of union sets and relations, the gist operation is performed
2247 =head3 Lexicographic Optimization
2249 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2250 the following functions
2251 compute a set that contains the lexicographic minimum or maximum
2252 of the elements in C<set> (or C<bset>) for those values of the parameters
2253 that satisfy C<dom>.
2254 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2255 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2257 In other words, the union of the parameter values
2258 for which the result is non-empty and of C<*empty>
2261 __isl_give isl_set *isl_basic_set_partial_lexmin(
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_basic_set_partial_lexmax(
2266 __isl_take isl_basic_set *bset,
2267 __isl_take isl_basic_set *dom,
2268 __isl_give isl_set **empty);
2269 __isl_give isl_set *isl_set_partial_lexmin(
2270 __isl_take isl_set *set, __isl_take isl_set *dom,
2271 __isl_give isl_set **empty);
2272 __isl_give isl_set *isl_set_partial_lexmax(
2273 __isl_take isl_set *set, __isl_take isl_set *dom,
2274 __isl_give isl_set **empty);
2276 Given a (basic) set C<set> (or C<bset>), the following functions simply
2277 return a set containing the lexicographic minimum or maximum
2278 of the elements in C<set> (or C<bset>).
2279 In case of union sets, the optimum is computed per space.
2281 __isl_give isl_set *isl_basic_set_lexmin(
2282 __isl_take isl_basic_set *bset);
2283 __isl_give isl_set *isl_basic_set_lexmax(
2284 __isl_take isl_basic_set *bset);
2285 __isl_give isl_set *isl_set_lexmin(
2286 __isl_take isl_set *set);
2287 __isl_give isl_set *isl_set_lexmax(
2288 __isl_take isl_set *set);
2289 __isl_give isl_union_set *isl_union_set_lexmin(
2290 __isl_take isl_union_set *uset);
2291 __isl_give isl_union_set *isl_union_set_lexmax(
2292 __isl_take isl_union_set *uset);
2294 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2295 the following functions
2296 compute a relation that maps each element of C<dom>
2297 to the single lexicographic minimum or maximum
2298 of the elements that are associated to that same
2299 element in C<map> (or C<bmap>).
2300 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2301 that contains the elements in C<dom> that do not map
2302 to any elements in C<map> (or C<bmap>).
2303 In other words, the union of the domain of the result and of C<*empty>
2306 __isl_give isl_map *isl_basic_map_partial_lexmax(
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_basic_map_partial_lexmin(
2311 __isl_take isl_basic_map *bmap,
2312 __isl_take isl_basic_set *dom,
2313 __isl_give isl_set **empty);
2314 __isl_give isl_map *isl_map_partial_lexmax(
2315 __isl_take isl_map *map, __isl_take isl_set *dom,
2316 __isl_give isl_set **empty);
2317 __isl_give isl_map *isl_map_partial_lexmin(
2318 __isl_take isl_map *map, __isl_take isl_set *dom,
2319 __isl_give isl_set **empty);
2321 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2322 return a map mapping each element in the domain of
2323 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2324 of all elements associated to that element.
2325 In case of union relations, the optimum is computed per space.
2327 __isl_give isl_map *isl_basic_map_lexmin(
2328 __isl_take isl_basic_map *bmap);
2329 __isl_give isl_map *isl_basic_map_lexmax(
2330 __isl_take isl_basic_map *bmap);
2331 __isl_give isl_map *isl_map_lexmin(
2332 __isl_take isl_map *map);
2333 __isl_give isl_map *isl_map_lexmax(
2334 __isl_take isl_map *map);
2335 __isl_give isl_union_map *isl_union_map_lexmin(
2336 __isl_take isl_union_map *umap);
2337 __isl_give isl_union_map *isl_union_map_lexmax(
2338 __isl_take isl_union_map *umap);
2342 Lists are defined over several element types, including
2343 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2344 Here we take lists of C<isl_set>s as an example.
2345 Lists can be created, copied and freed using the following functions.
2347 #include <isl/list.h>
2348 __isl_give isl_set_list *isl_set_list_from_set(
2349 __isl_take isl_set *el);
2350 __isl_give isl_set_list *isl_set_list_alloc(
2351 isl_ctx *ctx, int n);
2352 __isl_give isl_set_list *isl_set_list_copy(
2353 __isl_keep isl_set_list *list);
2354 __isl_give isl_set_list *isl_set_list_add(
2355 __isl_take isl_set_list *list,
2356 __isl_take isl_set *el);
2357 __isl_give isl_set_list *isl_set_list_concat(
2358 __isl_take isl_set_list *list1,
2359 __isl_take isl_set_list *list2);
2360 void *isl_set_list_free(__isl_take isl_set_list *list);
2362 C<isl_set_list_alloc> creates an empty list with a capacity for
2363 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2366 Lists can be inspected using the following functions.
2368 #include <isl/list.h>
2369 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2370 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2371 __isl_give isl_set *isl_set_list_get_set(
2372 __isl_keep isl_set_list *list, int index);
2373 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2374 int (*fn)(__isl_take isl_set *el, void *user),
2377 Lists can be printed using
2379 #include <isl/list.h>
2380 __isl_give isl_printer *isl_printer_print_set_list(
2381 __isl_take isl_printer *p,
2382 __isl_keep isl_set_list *list);
2386 Matrices can be created, copied and freed using the following functions.
2388 #include <isl/mat.h>
2389 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2390 unsigned n_row, unsigned n_col);
2391 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2392 void isl_mat_free(__isl_take isl_mat *mat);
2394 Note that the elements of a newly created matrix may have arbitrary values.
2395 The elements can be changed and inspected using the following functions.
2397 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2398 int isl_mat_rows(__isl_keep isl_mat *mat);
2399 int isl_mat_cols(__isl_keep isl_mat *mat);
2400 int isl_mat_get_element(__isl_keep isl_mat *mat,
2401 int row, int col, isl_int *v);
2402 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2403 int row, int col, isl_int v);
2404 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2405 int row, int col, int v);
2407 C<isl_mat_get_element> will return a negative value if anything went wrong.
2408 In that case, the value of C<*v> is undefined.
2410 The following function can be used to compute the (right) inverse
2411 of a matrix, i.e., a matrix such that the product of the original
2412 and the inverse (in that order) is a multiple of the identity matrix.
2413 The input matrix is assumed to be of full row-rank.
2415 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2417 The following function can be used to compute the (right) kernel
2418 (or null space) of a matrix, i.e., a matrix such that the product of
2419 the original and the kernel (in that order) is the zero matrix.
2421 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2423 =head2 Piecewise Quasi Affine Expressions
2425 The zero quasi affine expression can be created using
2427 __isl_give isl_aff *isl_aff_zero(
2428 __isl_take isl_local_space *ls);
2430 A quasi affine expression can also be initialized from an C<isl_div>:
2432 #include <isl/div.h>
2433 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2435 An empty piecewise quasi affine expression (one with no cells)
2436 or a piecewise quasi affine expression with a single cell can
2437 be created using the following functions.
2439 #include <isl/aff.h>
2440 __isl_give isl_pw_aff *isl_pw_aff_empty(
2441 __isl_take isl_space *space);
2442 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2443 __isl_take isl_set *set, __isl_take isl_aff *aff);
2444 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2445 __isl_take isl_aff *aff);
2447 Quasi affine expressions can be copied and freed using
2449 #include <isl/aff.h>
2450 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2451 void *isl_aff_free(__isl_take isl_aff *aff);
2453 __isl_give isl_pw_aff *isl_pw_aff_copy(
2454 __isl_keep isl_pw_aff *pwaff);
2455 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2457 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2458 using the following function. The constraint is required to have
2459 a non-zero coefficient for the specified dimension.
2461 #include <isl/constraint.h>
2462 __isl_give isl_aff *isl_constraint_get_bound(
2463 __isl_keep isl_constraint *constraint,
2464 enum isl_dim_type type, int pos);
2466 The entire affine expression of the constraint can also be extracted
2467 using the following function.
2469 #include <isl/constraint.h>
2470 __isl_give isl_aff *isl_constraint_get_aff(
2471 __isl_keep isl_constraint *constraint);
2473 Conversely, an equality constraint equating
2474 the affine expression to zero or an inequality constraint enforcing
2475 the affine expression to be non-negative, can be constructed using
2477 __isl_give isl_constraint *isl_equality_from_aff(
2478 __isl_take isl_aff *aff);
2479 __isl_give isl_constraint *isl_inequality_from_aff(
2480 __isl_take isl_aff *aff);
2482 The expression can be inspected using
2484 #include <isl/aff.h>
2485 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2486 int isl_aff_dim(__isl_keep isl_aff *aff,
2487 enum isl_dim_type type);
2488 __isl_give isl_local_space *isl_aff_get_local_space(
2489 __isl_keep isl_aff *aff);
2490 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2491 enum isl_dim_type type, unsigned pos);
2492 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2494 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2495 enum isl_dim_type type, int pos, isl_int *v);
2496 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2498 __isl_give isl_div *isl_aff_get_div(
2499 __isl_keep isl_aff *aff, int pos);
2501 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2502 int (*fn)(__isl_take isl_set *set,
2503 __isl_take isl_aff *aff,
2504 void *user), void *user);
2506 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2507 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2509 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2510 enum isl_dim_type type, unsigned first, unsigned n);
2511 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2512 enum isl_dim_type type, unsigned first, unsigned n);
2514 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2515 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2516 enum isl_dim_type type);
2517 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2519 It can be modified using
2521 #include <isl/aff.h>
2522 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2523 __isl_take isl_pw_aff *pwaff,
2524 __isl_take isl_id *id);
2525 __isl_give isl_aff *isl_aff_set_dim_name(
2526 __isl_take isl_aff *aff, enum isl_dim_type type,
2527 unsigned pos, const char *s);
2528 __isl_give isl_aff *isl_aff_set_constant(
2529 __isl_take isl_aff *aff, isl_int v);
2530 __isl_give isl_aff *isl_aff_set_constant_si(
2531 __isl_take isl_aff *aff, int v);
2532 __isl_give isl_aff *isl_aff_set_coefficient(
2533 __isl_take isl_aff *aff,
2534 enum isl_dim_type type, int pos, isl_int v);
2535 __isl_give isl_aff *isl_aff_set_coefficient_si(
2536 __isl_take isl_aff *aff,
2537 enum isl_dim_type type, int pos, int v);
2538 __isl_give isl_aff *isl_aff_set_denominator(
2539 __isl_take isl_aff *aff, isl_int v);
2541 __isl_give isl_aff *isl_aff_add_constant(
2542 __isl_take isl_aff *aff, isl_int v);
2543 __isl_give isl_aff *isl_aff_add_constant_si(
2544 __isl_take isl_aff *aff, int v);
2545 __isl_give isl_aff *isl_aff_add_coefficient(
2546 __isl_take isl_aff *aff,
2547 enum isl_dim_type type, int pos, isl_int v);
2548 __isl_give isl_aff *isl_aff_add_coefficient_si(
2549 __isl_take isl_aff *aff,
2550 enum isl_dim_type type, int pos, int v);
2552 __isl_give isl_aff *isl_aff_insert_dims(
2553 __isl_take isl_aff *aff,
2554 enum isl_dim_type type, unsigned first, unsigned n);
2555 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2556 __isl_take isl_pw_aff *pwaff,
2557 enum isl_dim_type type, unsigned first, unsigned n);
2558 __isl_give isl_aff *isl_aff_add_dims(
2559 __isl_take isl_aff *aff,
2560 enum isl_dim_type type, unsigned n);
2561 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2562 __isl_take isl_pw_aff *pwaff,
2563 enum isl_dim_type type, unsigned n);
2564 __isl_give isl_aff *isl_aff_drop_dims(
2565 __isl_take isl_aff *aff,
2566 enum isl_dim_type type, unsigned first, unsigned n);
2567 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2568 __isl_take isl_pw_aff *pwaff,
2569 enum isl_dim_type type, unsigned first, unsigned n);
2571 Note that the C<set_constant> and C<set_coefficient> functions
2572 set the I<numerator> of the constant or coefficient, while
2573 C<add_constant> and C<add_coefficient> add an integer value to
2574 the possibly rational constant or coefficient.
2576 To check whether an affine expressions is obviously zero
2577 or obviously equal to some other affine expression, use
2579 #include <isl/aff.h>
2580 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2581 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2582 __isl_keep isl_aff *aff2);
2586 #include <isl/aff.h>
2587 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2588 __isl_take isl_aff *aff2);
2589 __isl_give isl_pw_aff *isl_pw_aff_add(
2590 __isl_take isl_pw_aff *pwaff1,
2591 __isl_take isl_pw_aff *pwaff2);
2592 __isl_give isl_pw_aff *isl_pw_aff_min(
2593 __isl_take isl_pw_aff *pwaff1,
2594 __isl_take isl_pw_aff *pwaff2);
2595 __isl_give isl_pw_aff *isl_pw_aff_max(
2596 __isl_take isl_pw_aff *pwaff1,
2597 __isl_take isl_pw_aff *pwaff2);
2598 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2599 __isl_take isl_aff *aff2);
2600 __isl_give isl_pw_aff *isl_pw_aff_sub(
2601 __isl_take isl_pw_aff *pwaff1,
2602 __isl_take isl_pw_aff *pwaff2);
2603 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2604 __isl_give isl_pw_aff *isl_pw_aff_neg(
2605 __isl_take isl_pw_aff *pwaff);
2606 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2607 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2608 __isl_take isl_pw_aff *pwaff);
2609 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2610 __isl_give isl_pw_aff *isl_pw_aff_floor(
2611 __isl_take isl_pw_aff *pwaff);
2612 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2614 __isl_give isl_pw_aff *isl_pw_aff_mod(
2615 __isl_take isl_pw_aff *pwaff, isl_int mod);
2616 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2618 __isl_give isl_pw_aff *isl_pw_aff_scale(
2619 __isl_take isl_pw_aff *pwaff, isl_int f);
2620 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2622 __isl_give isl_aff *isl_aff_scale_down_ui(
2623 __isl_take isl_aff *aff, unsigned f);
2624 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2625 __isl_take isl_pw_aff *pwaff, isl_int f);
2627 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2628 __isl_take isl_pw_aff_list *list);
2629 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2630 __isl_take isl_pw_aff_list *list);
2632 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2633 __isl_take isl_pw_aff *pwqp);
2635 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2636 __isl_take isl_pw_aff *pwaff,
2637 __isl_take isl_space *model);
2639 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2640 __isl_take isl_set *context);
2641 __isl_give isl_pw_aff *isl_pw_aff_gist(
2642 __isl_take isl_pw_aff *pwaff,
2643 __isl_take isl_set *context);
2645 __isl_give isl_set *isl_pw_aff_domain(
2646 __isl_take isl_pw_aff *pwaff);
2648 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2649 __isl_take isl_aff *aff2);
2650 __isl_give isl_pw_aff *isl_pw_aff_mul(
2651 __isl_take isl_pw_aff *pwaff1,
2652 __isl_take isl_pw_aff *pwaff2);
2654 When multiplying two affine expressions, at least one of the two needs
2657 #include <isl/aff.h>
2658 __isl_give isl_basic_set *isl_aff_le_basic_set(
2659 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2660 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2661 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2662 __isl_give isl_set *isl_pw_aff_eq_set(
2663 __isl_take isl_pw_aff *pwaff1,
2664 __isl_take isl_pw_aff *pwaff2);
2665 __isl_give isl_set *isl_pw_aff_ne_set(
2666 __isl_take isl_pw_aff *pwaff1,
2667 __isl_take isl_pw_aff *pwaff2);
2668 __isl_give isl_set *isl_pw_aff_le_set(
2669 __isl_take isl_pw_aff *pwaff1,
2670 __isl_take isl_pw_aff *pwaff2);
2671 __isl_give isl_set *isl_pw_aff_lt_set(
2672 __isl_take isl_pw_aff *pwaff1,
2673 __isl_take isl_pw_aff *pwaff2);
2674 __isl_give isl_set *isl_pw_aff_ge_set(
2675 __isl_take isl_pw_aff *pwaff1,
2676 __isl_take isl_pw_aff *pwaff2);
2677 __isl_give isl_set *isl_pw_aff_gt_set(
2678 __isl_take isl_pw_aff *pwaff1,
2679 __isl_take isl_pw_aff *pwaff2);
2681 __isl_give isl_set *isl_pw_aff_list_eq_set(
2682 __isl_take isl_pw_aff_list *list1,
2683 __isl_take isl_pw_aff_list *list2);
2684 __isl_give isl_set *isl_pw_aff_list_ne_set(
2685 __isl_take isl_pw_aff_list *list1,
2686 __isl_take isl_pw_aff_list *list2);
2687 __isl_give isl_set *isl_pw_aff_list_le_set(
2688 __isl_take isl_pw_aff_list *list1,
2689 __isl_take isl_pw_aff_list *list2);
2690 __isl_give isl_set *isl_pw_aff_list_lt_set(
2691 __isl_take isl_pw_aff_list *list1,
2692 __isl_take isl_pw_aff_list *list2);
2693 __isl_give isl_set *isl_pw_aff_list_ge_set(
2694 __isl_take isl_pw_aff_list *list1,
2695 __isl_take isl_pw_aff_list *list2);
2696 __isl_give isl_set *isl_pw_aff_list_gt_set(
2697 __isl_take isl_pw_aff_list *list1,
2698 __isl_take isl_pw_aff_list *list2);
2700 The function C<isl_aff_ge_basic_set> returns a basic set
2701 containing those elements in the shared space
2702 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2703 The function C<isl_aff_ge_set> returns a set
2704 containing those elements in the shared domain
2705 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2706 The functions operating on C<isl_pw_aff_list> apply the corresponding
2707 C<isl_pw_aff> function to each pair of elements in the two lists.
2709 #include <isl/aff.h>
2710 __isl_give isl_set *isl_pw_aff_nonneg_set(
2711 __isl_take isl_pw_aff *pwaff);
2712 __isl_give isl_set *isl_pw_aff_zero_set(
2713 __isl_take isl_pw_aff *pwaff);
2714 __isl_give isl_set *isl_pw_aff_non_zero_set(
2715 __isl_take isl_pw_aff *pwaff);
2717 The function C<isl_pw_aff_nonneg_set> returns a set
2718 containing those elements in the domain
2719 of C<pwaff> where C<pwaff> is non-negative.
2721 #include <isl/aff.h>
2722 __isl_give isl_pw_aff *isl_pw_aff_cond(
2723 __isl_take isl_set *cond,
2724 __isl_take isl_pw_aff *pwaff_true,
2725 __isl_take isl_pw_aff *pwaff_false);
2727 The function C<isl_pw_aff_cond> performs a conditional operator
2728 and returns an expression that is equal to C<pwaff_true>
2729 for elements in C<cond> and equal to C<pwaff_false> for elements
2732 #include <isl/aff.h>
2733 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2734 __isl_take isl_pw_aff *pwaff1,
2735 __isl_take isl_pw_aff *pwaff2);
2736 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2737 __isl_take isl_pw_aff *pwaff1,
2738 __isl_take isl_pw_aff *pwaff2);
2740 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2741 expression with a domain that is the union of those of C<pwaff1> and
2742 C<pwaff2> and such that on each cell, the quasi-affine expression is
2743 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2744 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2745 associated expression is the defined one.
2747 An expression can be printed using
2749 #include <isl/aff.h>
2750 __isl_give isl_printer *isl_printer_print_aff(
2751 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2753 __isl_give isl_printer *isl_printer_print_pw_aff(
2754 __isl_take isl_printer *p,
2755 __isl_keep isl_pw_aff *pwaff);
2759 Points are elements of a set. They can be used to construct
2760 simple sets (boxes) or they can be used to represent the
2761 individual elements of a set.
2762 The zero point (the origin) can be created using
2764 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2766 The coordinates of a point can be inspected, set and changed
2769 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2770 enum isl_dim_type type, int pos, isl_int *v);
2771 __isl_give isl_point *isl_point_set_coordinate(
2772 __isl_take isl_point *pnt,
2773 enum isl_dim_type type, int pos, isl_int v);
2775 __isl_give isl_point *isl_point_add_ui(
2776 __isl_take isl_point *pnt,
2777 enum isl_dim_type type, int pos, unsigned val);
2778 __isl_give isl_point *isl_point_sub_ui(
2779 __isl_take isl_point *pnt,
2780 enum isl_dim_type type, int pos, unsigned val);
2782 Other properties can be obtained using
2784 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2786 Points can be copied or freed using
2788 __isl_give isl_point *isl_point_copy(
2789 __isl_keep isl_point *pnt);
2790 void isl_point_free(__isl_take isl_point *pnt);
2792 A singleton set can be created from a point using
2794 __isl_give isl_basic_set *isl_basic_set_from_point(
2795 __isl_take isl_point *pnt);
2796 __isl_give isl_set *isl_set_from_point(
2797 __isl_take isl_point *pnt);
2799 and a box can be created from two opposite extremal points using
2801 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2802 __isl_take isl_point *pnt1,
2803 __isl_take isl_point *pnt2);
2804 __isl_give isl_set *isl_set_box_from_points(
2805 __isl_take isl_point *pnt1,
2806 __isl_take isl_point *pnt2);
2808 All elements of a B<bounded> (union) set can be enumerated using
2809 the following functions.
2811 int isl_set_foreach_point(__isl_keep isl_set *set,
2812 int (*fn)(__isl_take isl_point *pnt, void *user),
2814 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2815 int (*fn)(__isl_take isl_point *pnt, void *user),
2818 The function C<fn> is called for each integer point in
2819 C<set> with as second argument the last argument of
2820 the C<isl_set_foreach_point> call. The function C<fn>
2821 should return C<0> on success and C<-1> on failure.
2822 In the latter case, C<isl_set_foreach_point> will stop
2823 enumerating and return C<-1> as well.
2824 If the enumeration is performed successfully and to completion,
2825 then C<isl_set_foreach_point> returns C<0>.
2827 To obtain a single point of a (basic) set, use
2829 __isl_give isl_point *isl_basic_set_sample_point(
2830 __isl_take isl_basic_set *bset);
2831 __isl_give isl_point *isl_set_sample_point(
2832 __isl_take isl_set *set);
2834 If C<set> does not contain any (integer) points, then the
2835 resulting point will be ``void'', a property that can be
2838 int isl_point_is_void(__isl_keep isl_point *pnt);
2840 =head2 Piecewise Quasipolynomials
2842 A piecewise quasipolynomial is a particular kind of function that maps
2843 a parametric point to a rational value.
2844 More specifically, a quasipolynomial is a polynomial expression in greatest
2845 integer parts of affine expressions of parameters and variables.
2846 A piecewise quasipolynomial is a subdivision of a given parametric
2847 domain into disjoint cells with a quasipolynomial associated to
2848 each cell. The value of the piecewise quasipolynomial at a given
2849 point is the value of the quasipolynomial associated to the cell
2850 that contains the point. Outside of the union of cells,
2851 the value is assumed to be zero.
2852 For example, the piecewise quasipolynomial
2854 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2856 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2857 A given piecewise quasipolynomial has a fixed domain dimension.
2858 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2859 defined over different domains.
2860 Piecewise quasipolynomials are mainly used by the C<barvinok>
2861 library for representing the number of elements in a parametric set or map.
2862 For example, the piecewise quasipolynomial above represents
2863 the number of points in the map
2865 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2867 =head3 Printing (Piecewise) Quasipolynomials
2869 Quasipolynomials and piecewise quasipolynomials can be printed
2870 using the following functions.
2872 __isl_give isl_printer *isl_printer_print_qpolynomial(
2873 __isl_take isl_printer *p,
2874 __isl_keep isl_qpolynomial *qp);
2876 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2877 __isl_take isl_printer *p,
2878 __isl_keep isl_pw_qpolynomial *pwqp);
2880 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2881 __isl_take isl_printer *p,
2882 __isl_keep isl_union_pw_qpolynomial *upwqp);
2884 The output format of the printer
2885 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2886 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2888 In case of printing in C<ISL_FORMAT_C>, the user may want
2889 to set the names of all dimensions
2891 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2892 __isl_take isl_qpolynomial *qp,
2893 enum isl_dim_type type, unsigned pos,
2895 __isl_give isl_pw_qpolynomial *
2896 isl_pw_qpolynomial_set_dim_name(
2897 __isl_take isl_pw_qpolynomial *pwqp,
2898 enum isl_dim_type type, unsigned pos,
2901 =head3 Creating New (Piecewise) Quasipolynomials
2903 Some simple quasipolynomials can be created using the following functions.
2904 More complicated quasipolynomials can be created by applying
2905 operations such as addition and multiplication
2906 on the resulting quasipolynomials
2908 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2909 __isl_take isl_space *dim);
2910 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2911 __isl_take isl_space *dim);
2912 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2913 __isl_take isl_space *dim);
2914 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2915 __isl_take isl_space *dim);
2916 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2917 __isl_take isl_space *dim);
2918 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2919 __isl_take isl_space *dim,
2920 const isl_int n, const isl_int d);
2921 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2922 __isl_take isl_div *div);
2923 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2924 __isl_take isl_space *dim,
2925 enum isl_dim_type type, unsigned pos);
2926 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2927 __isl_take isl_aff *aff);
2929 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2930 with a single cell can be created using the following functions.
2931 Multiple of these single cell piecewise quasipolynomials can
2932 be combined to create more complicated piecewise quasipolynomials.
2934 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2935 __isl_take isl_space *space);
2936 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2937 __isl_take isl_set *set,
2938 __isl_take isl_qpolynomial *qp);
2939 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2940 __isl_take isl_qpolynomial *qp);
2941 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2942 __isl_take isl_pw_aff *pwaff);
2944 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2945 __isl_take isl_space *space);
2946 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2947 __isl_take isl_pw_qpolynomial *pwqp);
2948 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2949 __isl_take isl_union_pw_qpolynomial *upwqp,
2950 __isl_take isl_pw_qpolynomial *pwqp);
2952 Quasipolynomials can be copied and freed again using the following
2955 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2956 __isl_keep isl_qpolynomial *qp);
2957 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2959 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2960 __isl_keep isl_pw_qpolynomial *pwqp);
2961 void *isl_pw_qpolynomial_free(
2962 __isl_take isl_pw_qpolynomial *pwqp);
2964 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2965 __isl_keep isl_union_pw_qpolynomial *upwqp);
2966 void isl_union_pw_qpolynomial_free(
2967 __isl_take isl_union_pw_qpolynomial *upwqp);
2969 =head3 Inspecting (Piecewise) Quasipolynomials
2971 To iterate over all piecewise quasipolynomials in a union
2972 piecewise quasipolynomial, use the following function
2974 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2975 __isl_keep isl_union_pw_qpolynomial *upwqp,
2976 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2979 To extract the piecewise quasipolynomial in a given space from a union, use
2981 __isl_give isl_pw_qpolynomial *
2982 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2983 __isl_keep isl_union_pw_qpolynomial *upwqp,
2984 __isl_take isl_space *space);
2986 To iterate over the cells in a piecewise quasipolynomial,
2987 use either of the following two functions
2989 int isl_pw_qpolynomial_foreach_piece(
2990 __isl_keep isl_pw_qpolynomial *pwqp,
2991 int (*fn)(__isl_take isl_set *set,
2992 __isl_take isl_qpolynomial *qp,
2993 void *user), void *user);
2994 int isl_pw_qpolynomial_foreach_lifted_piece(
2995 __isl_keep isl_pw_qpolynomial *pwqp,
2996 int (*fn)(__isl_take isl_set *set,
2997 __isl_take isl_qpolynomial *qp,
2998 void *user), void *user);
3000 As usual, the function C<fn> should return C<0> on success
3001 and C<-1> on failure. The difference between
3002 C<isl_pw_qpolynomial_foreach_piece> and
3003 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3004 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3005 compute unique representations for all existentially quantified
3006 variables and then turn these existentially quantified variables
3007 into extra set variables, adapting the associated quasipolynomial
3008 accordingly. This means that the C<set> passed to C<fn>
3009 will not have any existentially quantified variables, but that
3010 the dimensions of the sets may be different for different
3011 invocations of C<fn>.
3013 To iterate over all terms in a quasipolynomial,
3016 int isl_qpolynomial_foreach_term(
3017 __isl_keep isl_qpolynomial *qp,
3018 int (*fn)(__isl_take isl_term *term,
3019 void *user), void *user);
3021 The terms themselves can be inspected and freed using
3024 unsigned isl_term_dim(__isl_keep isl_term *term,
3025 enum isl_dim_type type);
3026 void isl_term_get_num(__isl_keep isl_term *term,
3028 void isl_term_get_den(__isl_keep isl_term *term,
3030 int isl_term_get_exp(__isl_keep isl_term *term,
3031 enum isl_dim_type type, unsigned pos);
3032 __isl_give isl_div *isl_term_get_div(
3033 __isl_keep isl_term *term, unsigned pos);
3034 void isl_term_free(__isl_take isl_term *term);
3036 Each term is a product of parameters, set variables and
3037 integer divisions. The function C<isl_term_get_exp>
3038 returns the exponent of a given dimensions in the given term.
3039 The C<isl_int>s in the arguments of C<isl_term_get_num>
3040 and C<isl_term_get_den> need to have been initialized
3041 using C<isl_int_init> before calling these functions.
3043 =head3 Properties of (Piecewise) Quasipolynomials
3045 To check whether a quasipolynomial is actually a constant,
3046 use the following function.
3048 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3049 isl_int *n, isl_int *d);
3051 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3052 then the numerator and denominator of the constant
3053 are returned in C<*n> and C<*d>, respectively.
3055 =head3 Operations on (Piecewise) Quasipolynomials
3057 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3058 __isl_take isl_qpolynomial *qp, isl_int v);
3059 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3060 __isl_take isl_qpolynomial *qp);
3061 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3062 __isl_take isl_qpolynomial *qp1,
3063 __isl_take isl_qpolynomial *qp2);
3064 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3065 __isl_take isl_qpolynomial *qp1,
3066 __isl_take isl_qpolynomial *qp2);
3067 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3068 __isl_take isl_qpolynomial *qp1,
3069 __isl_take isl_qpolynomial *qp2);
3070 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3071 __isl_take isl_qpolynomial *qp, unsigned exponent);
3073 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3074 __isl_take isl_pw_qpolynomial *pwqp1,
3075 __isl_take isl_pw_qpolynomial *pwqp2);
3076 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3077 __isl_take isl_pw_qpolynomial *pwqp1,
3078 __isl_take isl_pw_qpolynomial *pwqp2);
3079 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3080 __isl_take isl_pw_qpolynomial *pwqp1,
3081 __isl_take isl_pw_qpolynomial *pwqp2);
3082 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3083 __isl_take isl_pw_qpolynomial *pwqp);
3084 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3085 __isl_take isl_pw_qpolynomial *pwqp1,
3086 __isl_take isl_pw_qpolynomial *pwqp2);
3087 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3088 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3090 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3091 __isl_take isl_union_pw_qpolynomial *upwqp1,
3092 __isl_take isl_union_pw_qpolynomial *upwqp2);
3093 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3094 __isl_take isl_union_pw_qpolynomial *upwqp1,
3095 __isl_take isl_union_pw_qpolynomial *upwqp2);
3096 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3097 __isl_take isl_union_pw_qpolynomial *upwqp1,
3098 __isl_take isl_union_pw_qpolynomial *upwqp2);
3100 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3101 __isl_take isl_pw_qpolynomial *pwqp,
3102 __isl_take isl_point *pnt);
3104 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3105 __isl_take isl_union_pw_qpolynomial *upwqp,
3106 __isl_take isl_point *pnt);
3108 __isl_give isl_set *isl_pw_qpolynomial_domain(
3109 __isl_take isl_pw_qpolynomial *pwqp);
3110 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3111 __isl_take isl_pw_qpolynomial *pwpq,
3112 __isl_take isl_set *set);
3114 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3115 __isl_take isl_union_pw_qpolynomial *upwqp);
3116 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3117 __isl_take isl_union_pw_qpolynomial *upwpq,
3118 __isl_take isl_union_set *uset);
3120 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3121 __isl_take isl_qpolynomial *qp,
3122 __isl_take isl_space *model);
3124 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3125 __isl_take isl_union_pw_qpolynomial *upwqp);
3127 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3128 __isl_take isl_qpolynomial *qp,
3129 __isl_take isl_set *context);
3131 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3132 __isl_take isl_pw_qpolynomial *pwqp,
3133 __isl_take isl_set *context);
3135 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3136 __isl_take isl_union_pw_qpolynomial *upwqp,
3137 __isl_take isl_union_set *context);
3139 The gist operation applies the gist operation to each of
3140 the cells in the domain of the input piecewise quasipolynomial.
3141 The context is also exploited
3142 to simplify the quasipolynomials associated to each cell.
3144 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3145 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3146 __isl_give isl_union_pw_qpolynomial *
3147 isl_union_pw_qpolynomial_to_polynomial(
3148 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3150 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3151 the polynomial will be an overapproximation. If C<sign> is negative,
3152 it will be an underapproximation. If C<sign> is zero, the approximation
3153 will lie somewhere in between.
3155 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3157 A piecewise quasipolynomial reduction is a piecewise
3158 reduction (or fold) of quasipolynomials.
3159 In particular, the reduction can be maximum or a minimum.
3160 The objects are mainly used to represent the result of
3161 an upper or lower bound on a quasipolynomial over its domain,
3162 i.e., as the result of the following function.
3164 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3165 __isl_take isl_pw_qpolynomial *pwqp,
3166 enum isl_fold type, int *tight);
3168 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3169 __isl_take isl_union_pw_qpolynomial *upwqp,
3170 enum isl_fold type, int *tight);
3172 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3173 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3174 is the returned bound is known be tight, i.e., for each value
3175 of the parameters there is at least
3176 one element in the domain that reaches the bound.
3177 If the domain of C<pwqp> is not wrapping, then the bound is computed
3178 over all elements in that domain and the result has a purely parametric
3179 domain. If the domain of C<pwqp> is wrapping, then the bound is
3180 computed over the range of the wrapped relation. The domain of the
3181 wrapped relation becomes the domain of the result.
3183 A (piecewise) quasipolynomial reduction can be copied or freed using the
3184 following functions.
3186 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3187 __isl_keep isl_qpolynomial_fold *fold);
3188 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3189 __isl_keep isl_pw_qpolynomial_fold *pwf);
3190 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3191 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3192 void isl_qpolynomial_fold_free(
3193 __isl_take isl_qpolynomial_fold *fold);
3194 void *isl_pw_qpolynomial_fold_free(
3195 __isl_take isl_pw_qpolynomial_fold *pwf);
3196 void isl_union_pw_qpolynomial_fold_free(
3197 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3199 =head3 Printing Piecewise Quasipolynomial Reductions
3201 Piecewise quasipolynomial reductions can be printed
3202 using the following function.
3204 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3205 __isl_take isl_printer *p,
3206 __isl_keep isl_pw_qpolynomial_fold *pwf);
3207 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3208 __isl_take isl_printer *p,
3209 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3211 For C<isl_printer_print_pw_qpolynomial_fold>,
3212 output format of the printer
3213 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3214 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3215 output format of the printer
3216 needs to be set to C<ISL_FORMAT_ISL>.
3217 In case of printing in C<ISL_FORMAT_C>, the user may want
3218 to set the names of all dimensions
3220 __isl_give isl_pw_qpolynomial_fold *
3221 isl_pw_qpolynomial_fold_set_dim_name(
3222 __isl_take isl_pw_qpolynomial_fold *pwf,
3223 enum isl_dim_type type, unsigned pos,
3226 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3228 To iterate over all piecewise quasipolynomial reductions in a union
3229 piecewise quasipolynomial reduction, use the following function
3231 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3232 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3233 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3234 void *user), void *user);
3236 To iterate over the cells in a piecewise quasipolynomial reduction,
3237 use either of the following two functions
3239 int isl_pw_qpolynomial_fold_foreach_piece(
3240 __isl_keep isl_pw_qpolynomial_fold *pwf,
3241 int (*fn)(__isl_take isl_set *set,
3242 __isl_take isl_qpolynomial_fold *fold,
3243 void *user), void *user);
3244 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3245 __isl_keep isl_pw_qpolynomial_fold *pwf,
3246 int (*fn)(__isl_take isl_set *set,
3247 __isl_take isl_qpolynomial_fold *fold,
3248 void *user), void *user);
3250 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3251 of the difference between these two functions.
3253 To iterate over all quasipolynomials in a reduction, use
3255 int isl_qpolynomial_fold_foreach_qpolynomial(
3256 __isl_keep isl_qpolynomial_fold *fold,
3257 int (*fn)(__isl_take isl_qpolynomial *qp,
3258 void *user), void *user);
3260 =head3 Operations on Piecewise Quasipolynomial Reductions
3262 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3263 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3265 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3266 __isl_take isl_pw_qpolynomial_fold *pwf1,
3267 __isl_take isl_pw_qpolynomial_fold *pwf2);
3269 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3270 __isl_take isl_pw_qpolynomial_fold *pwf1,
3271 __isl_take isl_pw_qpolynomial_fold *pwf2);
3273 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3274 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3275 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3277 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3278 __isl_take isl_pw_qpolynomial_fold *pwf,
3279 __isl_take isl_point *pnt);
3281 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3282 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3283 __isl_take isl_point *pnt);
3285 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3286 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3287 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3288 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3289 __isl_take isl_union_set *uset);
3291 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3292 __isl_take isl_pw_qpolynomial_fold *pwf);
3294 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3295 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3297 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3298 __isl_take isl_pw_qpolynomial_fold *pwf,
3299 __isl_take isl_set *context);
3301 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3302 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3303 __isl_take isl_union_set *context);
3305 The gist operation applies the gist operation to each of
3306 the cells in the domain of the input piecewise quasipolynomial reduction.
3307 In future, the operation will also exploit the context
3308 to simplify the quasipolynomial reductions associated to each cell.
3310 __isl_give isl_pw_qpolynomial_fold *
3311 isl_set_apply_pw_qpolynomial_fold(
3312 __isl_take isl_set *set,
3313 __isl_take isl_pw_qpolynomial_fold *pwf,
3315 __isl_give isl_pw_qpolynomial_fold *
3316 isl_map_apply_pw_qpolynomial_fold(
3317 __isl_take isl_map *map,
3318 __isl_take isl_pw_qpolynomial_fold *pwf,
3320 __isl_give isl_union_pw_qpolynomial_fold *
3321 isl_union_set_apply_union_pw_qpolynomial_fold(
3322 __isl_take isl_union_set *uset,
3323 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3325 __isl_give isl_union_pw_qpolynomial_fold *
3326 isl_union_map_apply_union_pw_qpolynomial_fold(
3327 __isl_take isl_union_map *umap,
3328 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3331 The functions taking a map
3332 compose the given map with the given piecewise quasipolynomial reduction.
3333 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3334 over all elements in the intersection of the range of the map
3335 and the domain of the piecewise quasipolynomial reduction
3336 as a function of an element in the domain of the map.
3337 The functions taking a set compute a bound over all elements in the
3338 intersection of the set and the domain of the
3339 piecewise quasipolynomial reduction.
3341 =head2 Dependence Analysis
3343 C<isl> contains specialized functionality for performing
3344 array dataflow analysis. That is, given a I<sink> access relation
3345 and a collection of possible I<source> access relations,
3346 C<isl> can compute relations that describe
3347 for each iteration of the sink access, which iteration
3348 of which of the source access relations was the last
3349 to access the same data element before the given iteration
3351 To compute standard flow dependences, the sink should be
3352 a read, while the sources should be writes.
3353 If any of the source accesses are marked as being I<may>
3354 accesses, then there will be a dependence to the last
3355 I<must> access B<and> to any I<may> access that follows
3356 this last I<must> access.
3357 In particular, if I<all> sources are I<may> accesses,
3358 then memory based dependence analysis is performed.
3359 If, on the other hand, all sources are I<must> accesses,
3360 then value based dependence analysis is performed.
3362 #include <isl/flow.h>
3364 typedef int (*isl_access_level_before)(void *first, void *second);
3366 __isl_give isl_access_info *isl_access_info_alloc(
3367 __isl_take isl_map *sink,
3368 void *sink_user, isl_access_level_before fn,
3370 __isl_give isl_access_info *isl_access_info_add_source(
3371 __isl_take isl_access_info *acc,
3372 __isl_take isl_map *source, int must,
3374 void isl_access_info_free(__isl_take isl_access_info *acc);
3376 __isl_give isl_flow *isl_access_info_compute_flow(
3377 __isl_take isl_access_info *acc);
3379 int isl_flow_foreach(__isl_keep isl_flow *deps,
3380 int (*fn)(__isl_take isl_map *dep, int must,
3381 void *dep_user, void *user),
3383 __isl_give isl_map *isl_flow_get_no_source(
3384 __isl_keep isl_flow *deps, int must);
3385 void isl_flow_free(__isl_take isl_flow *deps);
3387 The function C<isl_access_info_compute_flow> performs the actual
3388 dependence analysis. The other functions are used to construct
3389 the input for this function or to read off the output.
3391 The input is collected in an C<isl_access_info>, which can
3392 be created through a call to C<isl_access_info_alloc>.
3393 The arguments to this functions are the sink access relation
3394 C<sink>, a token C<sink_user> used to identify the sink
3395 access to the user, a callback function for specifying the
3396 relative order of source and sink accesses, and the number
3397 of source access relations that will be added.
3398 The callback function has type C<int (*)(void *first, void *second)>.
3399 The function is called with two user supplied tokens identifying
3400 either a source or the sink and it should return the shared nesting
3401 level and the relative order of the two accesses.
3402 In particular, let I<n> be the number of loops shared by
3403 the two accesses. If C<first> precedes C<second> textually,
3404 then the function should return I<2 * n + 1>; otherwise,
3405 it should return I<2 * n>.
3406 The sources can be added to the C<isl_access_info> by performing
3407 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3408 C<must> indicates whether the source is a I<must> access
3409 or a I<may> access. Note that a multi-valued access relation
3410 should only be marked I<must> if every iteration in the domain
3411 of the relation accesses I<all> elements in its image.
3412 The C<source_user> token is again used to identify
3413 the source access. The range of the source access relation
3414 C<source> should have the same dimension as the range
3415 of the sink access relation.
3416 The C<isl_access_info_free> function should usually not be
3417 called explicitly, because it is called implicitly by
3418 C<isl_access_info_compute_flow>.
3420 The result of the dependence analysis is collected in an
3421 C<isl_flow>. There may be elements of
3422 the sink access for which no preceding source access could be
3423 found or for which all preceding sources are I<may> accesses.
3424 The relations containing these elements can be obtained through
3425 calls to C<isl_flow_get_no_source>, the first with C<must> set
3426 and the second with C<must> unset.
3427 In the case of standard flow dependence analysis,
3428 with the sink a read and the sources I<must> writes,
3429 the first relation corresponds to the reads from uninitialized
3430 array elements and the second relation is empty.
3431 The actual flow dependences can be extracted using
3432 C<isl_flow_foreach>. This function will call the user-specified
3433 callback function C<fn> for each B<non-empty> dependence between
3434 a source and the sink. The callback function is called
3435 with four arguments, the actual flow dependence relation
3436 mapping source iterations to sink iterations, a boolean that
3437 indicates whether it is a I<must> or I<may> dependence, a token
3438 identifying the source and an additional C<void *> with value
3439 equal to the third argument of the C<isl_flow_foreach> call.
3440 A dependence is marked I<must> if it originates from a I<must>
3441 source and if it is not followed by any I<may> sources.
3443 After finishing with an C<isl_flow>, the user should call
3444 C<isl_flow_free> to free all associated memory.
3446 A higher-level interface to dependence analysis is provided
3447 by the following function.
3449 #include <isl/flow.h>
3451 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3452 __isl_take isl_union_map *must_source,
3453 __isl_take isl_union_map *may_source,
3454 __isl_take isl_union_map *schedule,
3455 __isl_give isl_union_map **must_dep,
3456 __isl_give isl_union_map **may_dep,
3457 __isl_give isl_union_map **must_no_source,
3458 __isl_give isl_union_map **may_no_source);
3460 The arrays are identified by the tuple names of the ranges
3461 of the accesses. The iteration domains by the tuple names
3462 of the domains of the accesses and of the schedule.
3463 The relative order of the iteration domains is given by the
3464 schedule. The relations returned through C<must_no_source>
3465 and C<may_no_source> are subsets of C<sink>.
3466 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3467 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3468 any of the other arguments is treated as an error.
3472 B<The functionality described in this section is fairly new
3473 and may be subject to change.>
3475 The following function can be used to compute a schedule
3476 for a union of domains. The generated schedule respects
3477 all C<validity> dependences. That is, all dependence distances
3478 over these dependences in the scheduled space are lexicographically
3479 positive. The generated schedule schedule also tries to minimize
3480 the dependence distances over C<proximity> dependences.
3481 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3482 for groups of domains where the dependence distances have only
3483 non-negative values.
3484 The algorithm used to construct the schedule is similar to that
3487 #include <isl/schedule.h>
3488 __isl_give isl_schedule *isl_union_set_compute_schedule(
3489 __isl_take isl_union_set *domain,
3490 __isl_take isl_union_map *validity,
3491 __isl_take isl_union_map *proximity);
3492 void *isl_schedule_free(__isl_take isl_schedule *sched);
3494 A mapping from the domains to the scheduled space can be obtained
3495 from an C<isl_schedule> using the following function.
3497 __isl_give isl_union_map *isl_schedule_get_map(
3498 __isl_keep isl_schedule *sched);
3500 A representation of the schedule can be printed using
3502 __isl_give isl_printer *isl_printer_print_schedule(
3503 __isl_take isl_printer *p,
3504 __isl_keep isl_schedule *schedule);
3506 A representation of the schedule as a forest of bands can be obtained
3507 using the following function.
3509 __isl_give isl_band_list *isl_schedule_get_band_forest(
3510 __isl_keep isl_schedule *schedule);
3512 The list can be manipulated as explained in L<"Lists">.
3513 The bands inside the list can be copied and freed using the following
3516 #include <isl/band.h>
3517 __isl_give isl_band *isl_band_copy(
3518 __isl_keep isl_band *band);
3519 void *isl_band_free(__isl_take isl_band *band);
3521 Each band contains zero or more scheduling dimensions.
3522 These are referred to as the members of the band.
3523 The section of the schedule that corresponds to the band is
3524 referred to as the partial schedule of the band.
3525 For those nodes that participate in a band, the outer scheduling
3526 dimensions form the prefix schedule, while the inner scheduling
3527 dimensions form the suffix schedule.
3528 That is, if we take a cut of the band forest, then the union of
3529 the concatenations of the prefix, partial and suffix schedules of
3530 each band in the cut is equal to the entire schedule (modulo
3531 some possible padding at the end with zero scheduling dimensions).
3532 The properties of a band can be inspected using the following functions.
3534 #include <isl/band.h>
3535 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3537 int isl_band_has_children(__isl_keep isl_band *band);
3538 __isl_give isl_band_list *isl_band_get_children(
3539 __isl_keep isl_band *band);
3541 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3542 __isl_keep isl_band *band);
3543 __isl_give isl_union_map *isl_band_get_partial_schedule(
3544 __isl_keep isl_band *band);
3545 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3546 __isl_keep isl_band *band);
3548 int isl_band_n_member(__isl_keep isl_band *band);
3549 int isl_band_member_is_zero_distance(
3550 __isl_keep isl_band *band, int pos);
3552 Note that a scheduling dimension is considered to be ``zero
3553 distance'' if it does not carry any proximity dependences
3555 That is, if the dependence distances of the proximity
3556 dependences are all zero in that direction (for fixed
3557 iterations of outer bands).
3559 A representation of the band can be printed using
3561 #include <isl/band.h>
3562 __isl_give isl_printer *isl_printer_print_band(
3563 __isl_take isl_printer *p,
3564 __isl_keep isl_band *band);
3566 =head2 Parametric Vertex Enumeration
3568 The parametric vertex enumeration described in this section
3569 is mainly intended to be used internally and by the C<barvinok>
3572 #include <isl/vertices.h>
3573 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3574 __isl_keep isl_basic_set *bset);
3576 The function C<isl_basic_set_compute_vertices> performs the
3577 actual computation of the parametric vertices and the chamber
3578 decomposition and store the result in an C<isl_vertices> object.
3579 This information can be queried by either iterating over all
3580 the vertices or iterating over all the chambers or cells
3581 and then iterating over all vertices that are active on the chamber.
3583 int isl_vertices_foreach_vertex(
3584 __isl_keep isl_vertices *vertices,
3585 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3588 int isl_vertices_foreach_cell(
3589 __isl_keep isl_vertices *vertices,
3590 int (*fn)(__isl_take isl_cell *cell, void *user),
3592 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3593 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3596 Other operations that can be performed on an C<isl_vertices> object are
3599 isl_ctx *isl_vertices_get_ctx(
3600 __isl_keep isl_vertices *vertices);
3601 int isl_vertices_get_n_vertices(
3602 __isl_keep isl_vertices *vertices);
3603 void isl_vertices_free(__isl_take isl_vertices *vertices);
3605 Vertices can be inspected and destroyed using the following functions.
3607 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3608 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3609 __isl_give isl_basic_set *isl_vertex_get_domain(
3610 __isl_keep isl_vertex *vertex);
3611 __isl_give isl_basic_set *isl_vertex_get_expr(
3612 __isl_keep isl_vertex *vertex);
3613 void isl_vertex_free(__isl_take isl_vertex *vertex);
3615 C<isl_vertex_get_expr> returns a singleton parametric set describing
3616 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3618 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3619 B<rational> basic sets, so they should mainly be used for inspection
3620 and should not be mixed with integer sets.
3622 Chambers can be inspected and destroyed using the following functions.
3624 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3625 __isl_give isl_basic_set *isl_cell_get_domain(
3626 __isl_keep isl_cell *cell);
3627 void isl_cell_free(__isl_take isl_cell *cell);
3631 Although C<isl> is mainly meant to be used as a library,
3632 it also contains some basic applications that use some
3633 of the functionality of C<isl>.
3634 The input may be specified in either the L<isl format>
3635 or the L<PolyLib format>.
3637 =head2 C<isl_polyhedron_sample>
3639 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3640 an integer element of the polyhedron, if there is any.
3641 The first column in the output is the denominator and is always
3642 equal to 1. If the polyhedron contains no integer points,
3643 then a vector of length zero is printed.
3647 C<isl_pip> takes the same input as the C<example> program
3648 from the C<piplib> distribution, i.e., a set of constraints
3649 on the parameters, a line containing only -1 and finally a set
3650 of constraints on a parametric polyhedron.
3651 The coefficients of the parameters appear in the last columns
3652 (but before the final constant column).
3653 The output is the lexicographic minimum of the parametric polyhedron.
3654 As C<isl> currently does not have its own output format, the output
3655 is just a dump of the internal state.
3657 =head2 C<isl_polyhedron_minimize>
3659 C<isl_polyhedron_minimize> computes the minimum of some linear
3660 or affine objective function over the integer points in a polyhedron.
3661 If an affine objective function
3662 is given, then the constant should appear in the last column.
3664 =head2 C<isl_polytope_scan>
3666 Given a polytope, C<isl_polytope_scan> prints
3667 all integer points in the polytope.