3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
90 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
91 Some of the old names have been kept for backward compatibility,
92 but they will be removed in the future.
96 =head3 Changes since isl-0.07
100 =item * The function C<isl_pw_aff_max> has been renamed to
101 C<isl_pw_aff_union_max>.
107 The source of C<isl> can be obtained either as a tarball
108 or from the git repository. Both are available from
109 L<http://freshmeat.net/projects/isl/>.
110 The installation process depends on how you obtained
113 =head2 Installation from the git repository
117 =item 1 Clone or update the repository
119 The first time the source is obtained, you need to clone
122 git clone git://repo.or.cz/isl.git
124 To obtain updates, you need to pull in the latest changes
128 =item 2 Generate C<configure>
134 After performing the above steps, continue
135 with the L<Common installation instructions>.
137 =head2 Common installation instructions
141 =item 1 Obtain C<GMP>
143 Building C<isl> requires C<GMP>, including its headers files.
144 Your distribution may not provide these header files by default
145 and you may need to install a package called C<gmp-devel> or something
146 similar. Alternatively, C<GMP> can be built from
147 source, available from L<http://gmplib.org/>.
151 C<isl> uses the standard C<autoconf> C<configure> script.
156 optionally followed by some configure options.
157 A complete list of options can be obtained by running
161 Below we discuss some of the more common options.
163 C<isl> can optionally use C<piplib>, but no
164 C<piplib> functionality is currently used by default.
165 The C<--with-piplib> option can
166 be used to specify which C<piplib>
167 library to use, either an installed version (C<system>),
168 an externally built version (C<build>)
169 or no version (C<no>). The option C<build> is mostly useful
170 in C<configure> scripts of larger projects that bundle both C<isl>
177 Installation prefix for C<isl>
179 =item C<--with-gmp-prefix>
181 Installation prefix for C<GMP> (architecture-independent files).
183 =item C<--with-gmp-exec-prefix>
185 Installation prefix for C<GMP> (architecture-dependent files).
187 =item C<--with-piplib>
189 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
191 =item C<--with-piplib-prefix>
193 Installation prefix for C<system> C<piplib> (architecture-independent files).
195 =item C<--with-piplib-exec-prefix>
197 Installation prefix for C<system> C<piplib> (architecture-dependent files).
199 =item C<--with-piplib-builddir>
201 Location where C<build> C<piplib> was built.
209 =item 4 Install (optional)
217 =head2 Initialization
219 All manipulations of integer sets and relations occur within
220 the context of an C<isl_ctx>.
221 A given C<isl_ctx> can only be used within a single thread.
222 All arguments of a function are required to have been allocated
223 within the same context.
224 There are currently no functions available for moving an object
225 from one C<isl_ctx> to another C<isl_ctx>. This means that
226 there is currently no way of safely moving an object from one
227 thread to another, unless the whole C<isl_ctx> is moved.
229 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
230 freed using C<isl_ctx_free>.
231 All objects allocated within an C<isl_ctx> should be freed
232 before the C<isl_ctx> itself is freed.
234 isl_ctx *isl_ctx_alloc();
235 void isl_ctx_free(isl_ctx *ctx);
239 All operations on integers, mainly the coefficients
240 of the constraints describing the sets and relations,
241 are performed in exact integer arithmetic using C<GMP>.
242 However, to allow future versions of C<isl> to optionally
243 support fixed integer arithmetic, all calls to C<GMP>
244 are wrapped inside C<isl> specific macros.
245 The basic type is C<isl_int> and the operations below
246 are available on this type.
247 The meanings of these operations are essentially the same
248 as their C<GMP> C<mpz_> counterparts.
249 As always with C<GMP> types, C<isl_int>s need to be
250 initialized with C<isl_int_init> before they can be used
251 and they need to be released with C<isl_int_clear>
253 The user should not assume that an C<isl_int> is represented
254 as a C<mpz_t>, but should instead explicitly convert between
255 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
256 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
260 =item isl_int_init(i)
262 =item isl_int_clear(i)
264 =item isl_int_set(r,i)
266 =item isl_int_set_si(r,i)
268 =item isl_int_set_gmp(r,g)
270 =item isl_int_get_gmp(i,g)
272 =item isl_int_abs(r,i)
274 =item isl_int_neg(r,i)
276 =item isl_int_swap(i,j)
278 =item isl_int_swap_or_set(i,j)
280 =item isl_int_add_ui(r,i,j)
282 =item isl_int_sub_ui(r,i,j)
284 =item isl_int_add(r,i,j)
286 =item isl_int_sub(r,i,j)
288 =item isl_int_mul(r,i,j)
290 =item isl_int_mul_ui(r,i,j)
292 =item isl_int_addmul(r,i,j)
294 =item isl_int_submul(r,i,j)
296 =item isl_int_gcd(r,i,j)
298 =item isl_int_lcm(r,i,j)
300 =item isl_int_divexact(r,i,j)
302 =item isl_int_cdiv_q(r,i,j)
304 =item isl_int_fdiv_q(r,i,j)
306 =item isl_int_fdiv_r(r,i,j)
308 =item isl_int_fdiv_q_ui(r,i,j)
310 =item isl_int_read(r,s)
312 =item isl_int_print(out,i,width)
316 =item isl_int_cmp(i,j)
318 =item isl_int_cmp_si(i,si)
320 =item isl_int_eq(i,j)
322 =item isl_int_ne(i,j)
324 =item isl_int_lt(i,j)
326 =item isl_int_le(i,j)
328 =item isl_int_gt(i,j)
330 =item isl_int_ge(i,j)
332 =item isl_int_abs_eq(i,j)
334 =item isl_int_abs_ne(i,j)
336 =item isl_int_abs_lt(i,j)
338 =item isl_int_abs_gt(i,j)
340 =item isl_int_abs_ge(i,j)
342 =item isl_int_is_zero(i)
344 =item isl_int_is_one(i)
346 =item isl_int_is_negone(i)
348 =item isl_int_is_pos(i)
350 =item isl_int_is_neg(i)
352 =item isl_int_is_nonpos(i)
354 =item isl_int_is_nonneg(i)
356 =item isl_int_is_divisible_by(i,j)
360 =head2 Sets and Relations
362 C<isl> uses six types of objects for representing sets and relations,
363 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
364 C<isl_union_set> and C<isl_union_map>.
365 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
366 can be described as a conjunction of affine constraints, while
367 C<isl_set> and C<isl_map> represent unions of
368 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
369 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
370 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
371 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
372 where dimensions with different space names
373 (see L<Dimension Specifications>) are considered different as well.
374 The difference between sets and relations (maps) is that sets have
375 one set of variables, while relations have two sets of variables,
376 input variables and output variables.
378 =head2 Memory Management
380 Since a high-level operation on sets and/or relations usually involves
381 several substeps and since the user is usually not interested in
382 the intermediate results, most functions that return a new object
383 will also release all the objects passed as arguments.
384 If the user still wants to use one or more of these arguments
385 after the function call, she should pass along a copy of the
386 object rather than the object itself.
387 The user is then responsible for making sure that the original
388 object gets used somewhere else or is explicitly freed.
390 The arguments and return values of all documented functions are
391 annotated to make clear which arguments are released and which
392 arguments are preserved. In particular, the following annotations
399 C<__isl_give> means that a new object is returned.
400 The user should make sure that the returned pointer is
401 used exactly once as a value for an C<__isl_take> argument.
402 In between, it can be used as a value for as many
403 C<__isl_keep> arguments as the user likes.
404 There is one exception, and that is the case where the
405 pointer returned is C<NULL>. Is this case, the user
406 is free to use it as an C<__isl_take> argument or not.
410 C<__isl_take> means that the object the argument points to
411 is taken over by the function and may no longer be used
412 by the user as an argument to any other function.
413 The pointer value must be one returned by a function
414 returning an C<__isl_give> pointer.
415 If the user passes in a C<NULL> value, then this will
416 be treated as an error in the sense that the function will
417 not perform its usual operation. However, it will still
418 make sure that all the other C<__isl_take> arguments
423 C<__isl_keep> means that the function will only use the object
424 temporarily. After the function has finished, the user
425 can still use it as an argument to other functions.
426 A C<NULL> value will be treated in the same way as
427 a C<NULL> value for an C<__isl_take> argument.
433 Identifiers are used to identify both individual dimensions
434 and tuples of dimensions. They consist of a name and an optional
435 pointer. Identifiers with the same name but different pointer values
436 are considered to be distinct.
437 Identifiers can be constructed, copied, freed, inspected and printed
438 using the following functions.
441 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
442 __isl_keep const char *name, void *user);
443 __isl_give isl_id *isl_id_copy(isl_id *id);
444 void *isl_id_free(__isl_take isl_id *id);
446 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
447 void *isl_id_get_user(__isl_keep isl_id *id);
448 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
450 __isl_give isl_printer *isl_printer_print_id(
451 __isl_take isl_printer *p, __isl_keep isl_id *id);
453 Note that C<isl_id_get_name> returns a pointer to some internal
454 data structure, so the result can only be used while the
455 corresponding C<isl_id> is alive.
457 =head2 Dimension Specifications
459 Whenever a new set or relation is created from scratch,
460 its dimension needs to be specified using an C<isl_dim>.
463 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
464 unsigned nparam, unsigned n_in, unsigned n_out);
465 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
466 unsigned nparam, unsigned dim);
467 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
468 void isl_dim_free(__isl_take isl_dim *dim);
469 unsigned isl_dim_size(__isl_keep isl_dim *dim,
470 enum isl_dim_type type);
472 The dimension specification used for creating a set
473 needs to be created using C<isl_dim_set_alloc>, while
474 that for creating a relation
475 needs to be created using C<isl_dim_alloc>.
476 C<isl_dim_size> can be used
477 to find out the number of dimensions of each type in
478 a dimension specification, where type may be
479 C<isl_dim_param>, C<isl_dim_in> (only for relations),
480 C<isl_dim_out> (only for relations), C<isl_dim_set>
481 (only for sets) or C<isl_dim_all>.
483 It is often useful to create objects that live in the
484 same space as some other object. This can be accomplished
485 by creating the new objects
486 (see L<Creating New Sets and Relations> or
487 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
488 specification of the original object.
491 __isl_give isl_dim *isl_basic_set_get_dim(
492 __isl_keep isl_basic_set *bset);
493 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
495 #include <isl/union_set.h>
496 __isl_give isl_dim *isl_union_set_get_dim(
497 __isl_keep isl_union_set *uset);
500 __isl_give isl_dim *isl_basic_map_get_dim(
501 __isl_keep isl_basic_map *bmap);
502 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
504 #include <isl/union_map.h>
505 __isl_give isl_dim *isl_union_map_get_dim(
506 __isl_keep isl_union_map *umap);
508 #include <isl/constraint.h>
509 __isl_give isl_dim *isl_constraint_get_dim(
510 __isl_keep isl_constraint *constraint);
512 #include <isl/polynomial.h>
513 __isl_give isl_dim *isl_qpolynomial_get_dim(
514 __isl_keep isl_qpolynomial *qp);
515 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
516 __isl_keep isl_qpolynomial_fold *fold);
517 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
518 __isl_keep isl_pw_qpolynomial *pwqp);
519 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
520 __isl_keep isl_union_pw_qpolynomial *upwqp);
521 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
522 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
525 __isl_give isl_dim *isl_aff_get_dim(
526 __isl_keep isl_aff *aff);
527 __isl_give isl_dim *isl_pw_aff_get_dim(
528 __isl_keep isl_pw_aff *pwaff);
530 #include <isl/point.h>
531 __isl_give isl_dim *isl_point_get_dim(
532 __isl_keep isl_point *pnt);
534 The identifiers or names of the individual dimensions may be set or read off
535 using the following functions.
538 __isl_give isl_dim *isl_dim_set_dim_id(
539 __isl_take isl_dim *dim,
540 enum isl_dim_type type, unsigned pos,
541 __isl_take isl_id *id);
542 int isl_dim_has_dim_id(__isl_keep isl_dim *dim,
543 enum isl_dim_type type, unsigned pos);
544 __isl_give isl_id *isl_dim_get_dim_id(
545 __isl_keep isl_dim *dim,
546 enum isl_dim_type type, unsigned pos);
547 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
548 enum isl_dim_type type, unsigned pos,
549 __isl_keep const char *name);
550 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
551 enum isl_dim_type type, unsigned pos);
553 Note that C<isl_dim_get_name> returns a pointer to some internal
554 data structure, so the result can only be used while the
555 corresponding C<isl_dim> is alive.
556 Also note that every function that operates on two sets or relations
557 requires that both arguments have the same parameters. This also
558 means that if one of the arguments has named parameters, then the
559 other needs to have named parameters too and the names need to match.
560 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
561 arguments may have different parameters (as long as they are named),
562 in which case the result will have as parameters the union of the parameters of
565 Given the identifier of a dimension (typically a parameter),
566 its position can be obtained from the following function.
569 int isl_dim_find_dim_by_id(__isl_keep isl_dim *dim,
570 enum isl_dim_type type, __isl_keep isl_id *id);
572 The identifiers or names of entire spaces may be set or read off
573 using the following functions.
576 __isl_give isl_dim *isl_dim_set_tuple_id(
577 __isl_take isl_dim *dim,
578 enum isl_dim_type type, __isl_take isl_id *id);
579 __isl_give isl_dim *isl_dim_reset_tuple_id(
580 __isl_take isl_dim *dim, enum isl_dim_type type);
581 int isl_dim_has_tuple_id(__isl_keep isl_dim *dim,
582 enum isl_dim_type type);
583 __isl_give isl_id *isl_dim_get_tuple_id(
584 __isl_keep isl_dim *dim, enum isl_dim_type type);
585 __isl_give isl_dim *isl_dim_set_tuple_name(
586 __isl_take isl_dim *dim,
587 enum isl_dim_type type, const char *s);
588 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
589 enum isl_dim_type type);
591 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
592 or C<isl_dim_set>. As with C<isl_dim_get_name>,
593 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
595 Binary operations require the corresponding spaces of their arguments
596 to have the same name.
598 Spaces can be nested. In particular, the domain of a set or
599 the domain or range of a relation can be a nested relation.
600 The following functions can be used to construct and deconstruct
601 such nested dimension specifications.
604 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
605 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
606 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
608 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
609 be the dimension specification of a set, while that of
610 C<isl_dim_wrap> should be the dimension specification of a relation.
611 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
612 of a relation, while that of C<isl_dim_wrap> is the dimension specification
615 Dimension specifications can be created from other dimension
616 specifications using the following functions.
618 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
619 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
620 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
621 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
622 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
623 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
624 __isl_take isl_dim *right);
625 __isl_give isl_dim *isl_dim_align_params(
626 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
627 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
628 enum isl_dim_type type, unsigned pos, unsigned n);
629 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
630 enum isl_dim_type type, unsigned n);
631 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
632 enum isl_dim_type type, unsigned first, unsigned n);
633 __isl_give isl_dim *isl_dim_move(__isl_take isl_dim *dim,
634 enum isl_dim_type dst_type, unsigned dst_pos,
635 enum isl_dim_type src_type, unsigned src_pos,
637 __isl_give isl_dim *isl_dim_map_from_set(
638 __isl_take isl_dim *dim);
639 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
641 Note that if dimensions are added or removed from a space, then
642 the name and the internal structure are lost.
646 A local space is essentially a dimension specification with
647 zero or more existentially quantified variables.
648 The local space of a basic set or relation can be obtained
649 using the following functions.
652 __isl_give isl_local_space *isl_basic_set_get_local_space(
653 __isl_keep isl_basic_set *bset);
656 __isl_give isl_local_space *isl_basic_map_get_local_space(
657 __isl_keep isl_basic_map *bmap);
659 A new local space can be created from a dimension specification using
661 #include <isl/local_space.h>
662 __isl_give isl_local_space *isl_local_space_from_dim(
663 __isl_take isl_dim *dim);
665 They can be inspected, copied and freed using the following functions.
667 #include <isl/local_space.h>
668 isl_ctx *isl_local_space_get_ctx(
669 __isl_keep isl_local_space *ls);
670 int isl_local_space_dim(__isl_keep isl_local_space *ls,
671 enum isl_dim_type type);
672 const char *isl_local_space_get_dim_name(
673 __isl_keep isl_local_space *ls,
674 enum isl_dim_type type, unsigned pos);
675 __isl_give isl_local_space *isl_local_space_set_dim_name(
676 __isl_take isl_local_space *ls,
677 enum isl_dim_type type, unsigned pos, const char *s);
678 __isl_give isl_dim *isl_local_space_get_dim(
679 __isl_keep isl_local_space *ls);
680 __isl_give isl_div *isl_local_space_get_div(
681 __isl_keep isl_local_space *ls, int pos);
682 __isl_give isl_local_space *isl_local_space_copy(
683 __isl_keep isl_local_space *ls);
684 void *isl_local_space_free(__isl_take isl_local_space *ls);
686 Two local spaces can be compared using
688 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
689 __isl_keep isl_local_space *ls2);
691 Local spaces can be created from other local spaces
692 using the following functions.
694 __isl_give isl_local_space *isl_local_space_from_domain(
695 __isl_take isl_local_space *ls);
696 __isl_give isl_local_space *isl_local_space_add_dims(
697 __isl_take isl_local_space *ls,
698 enum isl_dim_type type, unsigned n);
699 __isl_give isl_local_space *isl_local_space_insert_dims(
700 __isl_take isl_local_space *ls,
701 enum isl_dim_type type, unsigned first, unsigned n);
702 __isl_give isl_local_space *isl_local_space_drop_dims(
703 __isl_take isl_local_space *ls,
704 enum isl_dim_type type, unsigned first, unsigned n);
706 =head2 Input and Output
708 C<isl> supports its own input/output format, which is similar
709 to the C<Omega> format, but also supports the C<PolyLib> format
714 The C<isl> format is similar to that of C<Omega>, but has a different
715 syntax for describing the parameters and allows for the definition
716 of an existentially quantified variable as the integer division
717 of an affine expression.
718 For example, the set of integers C<i> between C<0> and C<n>
719 such that C<i % 10 <= 6> can be described as
721 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
724 A set or relation can have several disjuncts, separated
725 by the keyword C<or>. Each disjunct is either a conjunction
726 of constraints or a projection (C<exists>) of a conjunction
727 of constraints. The constraints are separated by the keyword
730 =head3 C<PolyLib> format
732 If the represented set is a union, then the first line
733 contains a single number representing the number of disjuncts.
734 Otherwise, a line containing the number C<1> is optional.
736 Each disjunct is represented by a matrix of constraints.
737 The first line contains two numbers representing
738 the number of rows and columns,
739 where the number of rows is equal to the number of constraints
740 and the number of columns is equal to two plus the number of variables.
741 The following lines contain the actual rows of the constraint matrix.
742 In each row, the first column indicates whether the constraint
743 is an equality (C<0>) or inequality (C<1>). The final column
744 corresponds to the constant term.
746 If the set is parametric, then the coefficients of the parameters
747 appear in the last columns before the constant column.
748 The coefficients of any existentially quantified variables appear
749 between those of the set variables and those of the parameters.
751 =head3 Extended C<PolyLib> format
753 The extended C<PolyLib> format is nearly identical to the
754 C<PolyLib> format. The only difference is that the line
755 containing the number of rows and columns of a constraint matrix
756 also contains four additional numbers:
757 the number of output dimensions, the number of input dimensions,
758 the number of local dimensions (i.e., the number of existentially
759 quantified variables) and the number of parameters.
760 For sets, the number of ``output'' dimensions is equal
761 to the number of set dimensions, while the number of ``input''
767 __isl_give isl_basic_set *isl_basic_set_read_from_file(
768 isl_ctx *ctx, FILE *input, int nparam);
769 __isl_give isl_basic_set *isl_basic_set_read_from_str(
770 isl_ctx *ctx, const char *str, int nparam);
771 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
772 FILE *input, int nparam);
773 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
774 const char *str, int nparam);
777 __isl_give isl_basic_map *isl_basic_map_read_from_file(
778 isl_ctx *ctx, FILE *input, int nparam);
779 __isl_give isl_basic_map *isl_basic_map_read_from_str(
780 isl_ctx *ctx, const char *str, int nparam);
781 __isl_give isl_map *isl_map_read_from_file(
782 isl_ctx *ctx, FILE *input, int nparam);
783 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
784 const char *str, int nparam);
786 #include <isl/union_set.h>
787 __isl_give isl_union_set *isl_union_set_read_from_file(
788 isl_ctx *ctx, FILE *input);
789 __isl_give isl_union_set *isl_union_set_read_from_str(
790 isl_ctx *ctx, const char *str);
792 #include <isl/union_map.h>
793 __isl_give isl_union_map *isl_union_map_read_from_file(
794 isl_ctx *ctx, FILE *input);
795 __isl_give isl_union_map *isl_union_map_read_from_str(
796 isl_ctx *ctx, const char *str);
798 The input format is autodetected and may be either the C<PolyLib> format
799 or the C<isl> format.
800 C<nparam> specifies how many of the final columns in
801 the C<PolyLib> format correspond to parameters.
802 If input is given in the C<isl> format, then the number
803 of parameters needs to be equal to C<nparam>.
804 If C<nparam> is negative, then any number of parameters
805 is accepted in the C<isl> format and zero parameters
806 are assumed in the C<PolyLib> format.
810 Before anything can be printed, an C<isl_printer> needs to
813 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
815 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
816 void isl_printer_free(__isl_take isl_printer *printer);
817 __isl_give char *isl_printer_get_str(
818 __isl_keep isl_printer *printer);
820 The behavior of the printer can be modified in various ways
822 __isl_give isl_printer *isl_printer_set_output_format(
823 __isl_take isl_printer *p, int output_format);
824 __isl_give isl_printer *isl_printer_set_indent(
825 __isl_take isl_printer *p, int indent);
826 __isl_give isl_printer *isl_printer_indent(
827 __isl_take isl_printer *p, int indent);
828 __isl_give isl_printer *isl_printer_set_prefix(
829 __isl_take isl_printer *p, const char *prefix);
830 __isl_give isl_printer *isl_printer_set_suffix(
831 __isl_take isl_printer *p, const char *suffix);
833 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
834 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
835 and defaults to C<ISL_FORMAT_ISL>.
836 Each line in the output is indented by C<indent> (set by
837 C<isl_printer_set_indent>) spaces
838 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
839 In the C<PolyLib> format output,
840 the coefficients of the existentially quantified variables
841 appear between those of the set variables and those
843 The function C<isl_printer_indent> increases the indentation
844 by the specified amount (which may be negative).
846 To actually print something, use
849 __isl_give isl_printer *isl_printer_print_basic_set(
850 __isl_take isl_printer *printer,
851 __isl_keep isl_basic_set *bset);
852 __isl_give isl_printer *isl_printer_print_set(
853 __isl_take isl_printer *printer,
854 __isl_keep isl_set *set);
857 __isl_give isl_printer *isl_printer_print_basic_map(
858 __isl_take isl_printer *printer,
859 __isl_keep isl_basic_map *bmap);
860 __isl_give isl_printer *isl_printer_print_map(
861 __isl_take isl_printer *printer,
862 __isl_keep isl_map *map);
864 #include <isl/union_set.h>
865 __isl_give isl_printer *isl_printer_print_union_set(
866 __isl_take isl_printer *p,
867 __isl_keep isl_union_set *uset);
869 #include <isl/union_map.h>
870 __isl_give isl_printer *isl_printer_print_union_map(
871 __isl_take isl_printer *p,
872 __isl_keep isl_union_map *umap);
874 When called on a file printer, the following function flushes
875 the file. When called on a string printer, the buffer is cleared.
877 __isl_give isl_printer *isl_printer_flush(
878 __isl_take isl_printer *p);
880 =head2 Creating New Sets and Relations
882 C<isl> has functions for creating some standard sets and relations.
886 =item * Empty sets and relations
888 __isl_give isl_basic_set *isl_basic_set_empty(
889 __isl_take isl_dim *dim);
890 __isl_give isl_basic_map *isl_basic_map_empty(
891 __isl_take isl_dim *dim);
892 __isl_give isl_set *isl_set_empty(
893 __isl_take isl_dim *dim);
894 __isl_give isl_map *isl_map_empty(
895 __isl_take isl_dim *dim);
896 __isl_give isl_union_set *isl_union_set_empty(
897 __isl_take isl_dim *dim);
898 __isl_give isl_union_map *isl_union_map_empty(
899 __isl_take isl_dim *dim);
901 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
902 is only used to specify the parameters.
904 =item * Universe sets and relations
906 __isl_give isl_basic_set *isl_basic_set_universe(
907 __isl_take isl_dim *dim);
908 __isl_give isl_basic_map *isl_basic_map_universe(
909 __isl_take isl_dim *dim);
910 __isl_give isl_set *isl_set_universe(
911 __isl_take isl_dim *dim);
912 __isl_give isl_map *isl_map_universe(
913 __isl_take isl_dim *dim);
914 __isl_give isl_union_set *isl_union_set_universe(
915 __isl_take isl_union_set *uset);
916 __isl_give isl_union_map *isl_union_map_universe(
917 __isl_take isl_union_map *umap);
919 The sets and relations constructed by the functions above
920 contain all integer values, while those constructed by the
921 functions below only contain non-negative values.
923 __isl_give isl_basic_set *isl_basic_set_nat_universe(
924 __isl_take isl_dim *dim);
925 __isl_give isl_basic_map *isl_basic_map_nat_universe(
926 __isl_take isl_dim *dim);
927 __isl_give isl_set *isl_set_nat_universe(
928 __isl_take isl_dim *dim);
929 __isl_give isl_map *isl_map_nat_universe(
930 __isl_take isl_dim *dim);
932 =item * Identity relations
934 __isl_give isl_basic_map *isl_basic_map_identity(
935 __isl_take isl_dim *dim);
936 __isl_give isl_map *isl_map_identity(
937 __isl_take isl_dim *dim);
939 The number of input and output dimensions in C<dim> needs
942 =item * Lexicographic order
944 __isl_give isl_map *isl_map_lex_lt(
945 __isl_take isl_dim *set_dim);
946 __isl_give isl_map *isl_map_lex_le(
947 __isl_take isl_dim *set_dim);
948 __isl_give isl_map *isl_map_lex_gt(
949 __isl_take isl_dim *set_dim);
950 __isl_give isl_map *isl_map_lex_ge(
951 __isl_take isl_dim *set_dim);
952 __isl_give isl_map *isl_map_lex_lt_first(
953 __isl_take isl_dim *dim, unsigned n);
954 __isl_give isl_map *isl_map_lex_le_first(
955 __isl_take isl_dim *dim, unsigned n);
956 __isl_give isl_map *isl_map_lex_gt_first(
957 __isl_take isl_dim *dim, unsigned n);
958 __isl_give isl_map *isl_map_lex_ge_first(
959 __isl_take isl_dim *dim, unsigned n);
961 The first four functions take a dimension specification for a B<set>
962 and return relations that express that the elements in the domain
963 are lexicographically less
964 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
965 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
966 than the elements in the range.
967 The last four functions take a dimension specification for a map
968 and return relations that express that the first C<n> dimensions
969 in the domain are lexicographically less
970 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
971 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
972 than the first C<n> dimensions in the range.
976 A basic set or relation can be converted to a set or relation
977 using the following functions.
979 __isl_give isl_set *isl_set_from_basic_set(
980 __isl_take isl_basic_set *bset);
981 __isl_give isl_map *isl_map_from_basic_map(
982 __isl_take isl_basic_map *bmap);
984 Sets and relations can be converted to union sets and relations
985 using the following functions.
987 __isl_give isl_union_map *isl_union_map_from_map(
988 __isl_take isl_map *map);
989 __isl_give isl_union_set *isl_union_set_from_set(
990 __isl_take isl_set *set);
992 The inverse conversions below can only be used if the input
993 union set or relation is known to contain elements in exactly one
996 __isl_give isl_set *isl_set_from_union_set(
997 __isl_take isl_union_set *uset);
998 __isl_give isl_map *isl_map_from_union_map(
999 __isl_take isl_union_map *umap);
1001 Sets and relations can be copied and freed again using the following
1004 __isl_give isl_basic_set *isl_basic_set_copy(
1005 __isl_keep isl_basic_set *bset);
1006 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1007 __isl_give isl_union_set *isl_union_set_copy(
1008 __isl_keep isl_union_set *uset);
1009 __isl_give isl_basic_map *isl_basic_map_copy(
1010 __isl_keep isl_basic_map *bmap);
1011 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1012 __isl_give isl_union_map *isl_union_map_copy(
1013 __isl_keep isl_union_map *umap);
1014 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1015 void isl_set_free(__isl_take isl_set *set);
1016 void *isl_union_set_free(__isl_take isl_union_set *uset);
1017 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1018 void isl_map_free(__isl_take isl_map *map);
1019 void *isl_union_map_free(__isl_take isl_union_map *umap);
1021 Other sets and relations can be constructed by starting
1022 from a universe set or relation, adding equality and/or
1023 inequality constraints and then projecting out the
1024 existentially quantified variables, if any.
1025 Constraints can be constructed, manipulated and
1026 added to (or removed from) (basic) sets and relations
1027 using the following functions.
1029 #include <isl/constraint.h>
1030 __isl_give isl_constraint *isl_equality_alloc(
1031 __isl_take isl_dim *dim);
1032 __isl_give isl_constraint *isl_inequality_alloc(
1033 __isl_take isl_dim *dim);
1034 __isl_give isl_constraint *isl_constraint_set_constant(
1035 __isl_take isl_constraint *constraint, isl_int v);
1036 __isl_give isl_constraint *isl_constraint_set_constant_si(
1037 __isl_take isl_constraint *constraint, int v);
1038 __isl_give isl_constraint *isl_constraint_set_coefficient(
1039 __isl_take isl_constraint *constraint,
1040 enum isl_dim_type type, int pos, isl_int v);
1041 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1042 __isl_take isl_constraint *constraint,
1043 enum isl_dim_type type, int pos, int v);
1044 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1045 __isl_take isl_basic_map *bmap,
1046 __isl_take isl_constraint *constraint);
1047 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1048 __isl_take isl_basic_set *bset,
1049 __isl_take isl_constraint *constraint);
1050 __isl_give isl_map *isl_map_add_constraint(
1051 __isl_take isl_map *map,
1052 __isl_take isl_constraint *constraint);
1053 __isl_give isl_set *isl_set_add_constraint(
1054 __isl_take isl_set *set,
1055 __isl_take isl_constraint *constraint);
1056 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1057 __isl_take isl_basic_set *bset,
1058 __isl_take isl_constraint *constraint);
1060 For example, to create a set containing the even integers
1061 between 10 and 42, you would use the following code.
1066 isl_basic_set *bset;
1069 dim = isl_dim_set_alloc(ctx, 0, 2);
1070 bset = isl_basic_set_universe(isl_dim_copy(dim));
1072 c = isl_equality_alloc(isl_dim_copy(dim));
1073 isl_int_set_si(v, -1);
1074 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1075 isl_int_set_si(v, 2);
1076 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1077 bset = isl_basic_set_add_constraint(bset, c);
1079 c = isl_inequality_alloc(isl_dim_copy(dim));
1080 isl_int_set_si(v, -10);
1081 isl_constraint_set_constant(c, v);
1082 isl_int_set_si(v, 1);
1083 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1084 bset = isl_basic_set_add_constraint(bset, c);
1086 c = isl_inequality_alloc(dim);
1087 isl_int_set_si(v, 42);
1088 isl_constraint_set_constant(c, v);
1089 isl_int_set_si(v, -1);
1090 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1091 bset = isl_basic_set_add_constraint(bset, c);
1093 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1099 isl_basic_set *bset;
1100 bset = isl_basic_set_read_from_str(ctx,
1101 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1103 A basic set or relation can also be constructed from two matrices
1104 describing the equalities and the inequalities.
1106 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1107 __isl_take isl_dim *dim,
1108 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1109 enum isl_dim_type c1,
1110 enum isl_dim_type c2, enum isl_dim_type c3,
1111 enum isl_dim_type c4);
1112 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1113 __isl_take isl_dim *dim,
1114 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1115 enum isl_dim_type c1,
1116 enum isl_dim_type c2, enum isl_dim_type c3,
1117 enum isl_dim_type c4, enum isl_dim_type c5);
1119 The C<isl_dim_type> arguments indicate the order in which
1120 different kinds of variables appear in the input matrices
1121 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1122 C<isl_dim_set> and C<isl_dim_div> for sets and
1123 of C<isl_dim_cst>, C<isl_dim_param>,
1124 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1126 A (basic) relation can also be constructed from a (piecewise) affine expression
1127 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1129 __isl_give isl_basic_map *isl_basic_map_from_aff(
1130 __isl_take isl_aff *aff);
1131 __isl_give isl_map *isl_map_from_pw_aff(
1132 __isl_take isl_pw_aff *pwaff);
1133 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1134 __isl_take isl_dim *domain_dim,
1135 __isl_take isl_aff_list *list);
1137 The C<domain_dim> argument describes the domain of the resulting
1138 basic relation. It is required because the C<list> may consist
1139 of zero affine expressions.
1141 =head2 Inspecting Sets and Relations
1143 Usually, the user should not have to care about the actual constraints
1144 of the sets and maps, but should instead apply the abstract operations
1145 explained in the following sections.
1146 Occasionally, however, it may be required to inspect the individual
1147 coefficients of the constraints. This section explains how to do so.
1148 In these cases, it may also be useful to have C<isl> compute
1149 an explicit representation of the existentially quantified variables.
1151 __isl_give isl_set *isl_set_compute_divs(
1152 __isl_take isl_set *set);
1153 __isl_give isl_map *isl_map_compute_divs(
1154 __isl_take isl_map *map);
1155 __isl_give isl_union_set *isl_union_set_compute_divs(
1156 __isl_take isl_union_set *uset);
1157 __isl_give isl_union_map *isl_union_map_compute_divs(
1158 __isl_take isl_union_map *umap);
1160 This explicit representation defines the existentially quantified
1161 variables as integer divisions of the other variables, possibly
1162 including earlier existentially quantified variables.
1163 An explicitly represented existentially quantified variable therefore
1164 has a unique value when the values of the other variables are known.
1165 If, furthermore, the same existentials, i.e., existentials
1166 with the same explicit representations, should appear in the
1167 same order in each of the disjuncts of a set or map, then the user should call
1168 either of the following functions.
1170 __isl_give isl_set *isl_set_align_divs(
1171 __isl_take isl_set *set);
1172 __isl_give isl_map *isl_map_align_divs(
1173 __isl_take isl_map *map);
1175 Alternatively, the existentially quantified variables can be removed
1176 using the following functions, which compute an overapproximation.
1178 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1179 __isl_take isl_basic_set *bset);
1180 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1181 __isl_take isl_basic_map *bmap);
1182 __isl_give isl_set *isl_set_remove_divs(
1183 __isl_take isl_set *set);
1184 __isl_give isl_map *isl_map_remove_divs(
1185 __isl_take isl_map *map);
1187 To iterate over all the sets or maps in a union set or map, use
1189 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1190 int (*fn)(__isl_take isl_set *set, void *user),
1192 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1193 int (*fn)(__isl_take isl_map *map, void *user),
1196 The number of sets or maps in a union set or map can be obtained
1199 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1200 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1202 To extract the set or map from a union with a given dimension
1205 __isl_give isl_set *isl_union_set_extract_set(
1206 __isl_keep isl_union_set *uset,
1207 __isl_take isl_dim *dim);
1208 __isl_give isl_map *isl_union_map_extract_map(
1209 __isl_keep isl_union_map *umap,
1210 __isl_take isl_dim *dim);
1212 To iterate over all the basic sets or maps in a set or map, use
1214 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1215 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1217 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1218 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1221 The callback function C<fn> should return 0 if successful and
1222 -1 if an error occurs. In the latter case, or if any other error
1223 occurs, the above functions will return -1.
1225 It should be noted that C<isl> does not guarantee that
1226 the basic sets or maps passed to C<fn> are disjoint.
1227 If this is required, then the user should call one of
1228 the following functions first.
1230 __isl_give isl_set *isl_set_make_disjoint(
1231 __isl_take isl_set *set);
1232 __isl_give isl_map *isl_map_make_disjoint(
1233 __isl_take isl_map *map);
1235 The number of basic sets in a set can be obtained
1238 int isl_set_n_basic_set(__isl_keep isl_set *set);
1240 To iterate over the constraints of a basic set or map, use
1242 #include <isl/constraint.h>
1244 int isl_basic_map_foreach_constraint(
1245 __isl_keep isl_basic_map *bmap,
1246 int (*fn)(__isl_take isl_constraint *c, void *user),
1248 void *isl_constraint_free(__isl_take isl_constraint *c);
1250 Again, the callback function C<fn> should return 0 if successful and
1251 -1 if an error occurs. In the latter case, or if any other error
1252 occurs, the above functions will return -1.
1253 The constraint C<c> represents either an equality or an inequality.
1254 Use the following function to find out whether a constraint
1255 represents an equality. If not, it represents an inequality.
1257 int isl_constraint_is_equality(
1258 __isl_keep isl_constraint *constraint);
1260 The coefficients of the constraints can be inspected using
1261 the following functions.
1263 void isl_constraint_get_constant(
1264 __isl_keep isl_constraint *constraint, isl_int *v);
1265 void isl_constraint_get_coefficient(
1266 __isl_keep isl_constraint *constraint,
1267 enum isl_dim_type type, int pos, isl_int *v);
1268 int isl_constraint_involves_dims(
1269 __isl_keep isl_constraint *constraint,
1270 enum isl_dim_type type, unsigned first, unsigned n);
1272 The explicit representations of the existentially quantified
1273 variables can be inspected using the following functions.
1274 Note that the user is only allowed to use these functions
1275 if the inspected set or map is the result of a call
1276 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1278 __isl_give isl_div *isl_constraint_div(
1279 __isl_keep isl_constraint *constraint, int pos);
1280 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1281 void isl_div_get_constant(__isl_keep isl_div *div,
1283 void isl_div_get_denominator(__isl_keep isl_div *div,
1285 void isl_div_get_coefficient(__isl_keep isl_div *div,
1286 enum isl_dim_type type, int pos, isl_int *v);
1288 To obtain the constraints of a basic set or map in matrix
1289 form, use the following functions.
1291 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1292 __isl_keep isl_basic_set *bset,
1293 enum isl_dim_type c1, enum isl_dim_type c2,
1294 enum isl_dim_type c3, enum isl_dim_type c4);
1295 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1296 __isl_keep isl_basic_set *bset,
1297 enum isl_dim_type c1, enum isl_dim_type c2,
1298 enum isl_dim_type c3, enum isl_dim_type c4);
1299 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1300 __isl_keep isl_basic_map *bmap,
1301 enum isl_dim_type c1,
1302 enum isl_dim_type c2, enum isl_dim_type c3,
1303 enum isl_dim_type c4, enum isl_dim_type c5);
1304 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1305 __isl_keep isl_basic_map *bmap,
1306 enum isl_dim_type c1,
1307 enum isl_dim_type c2, enum isl_dim_type c3,
1308 enum isl_dim_type c4, enum isl_dim_type c5);
1310 The C<isl_dim_type> arguments dictate the order in which
1311 different kinds of variables appear in the resulting matrix
1312 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1313 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1315 The number of parameters, input, output or set dimensions can
1316 be obtained using the following functions.
1318 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1319 enum isl_dim_type type);
1320 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1321 enum isl_dim_type type);
1322 unsigned isl_set_dim(__isl_keep isl_set *set,
1323 enum isl_dim_type type);
1324 unsigned isl_map_dim(__isl_keep isl_map *map,
1325 enum isl_dim_type type);
1327 To check whether the description of a set or relation depends
1328 on one or more given dimensions, it is not necessary to iterate over all
1329 constraints. Instead the following functions can be used.
1331 int isl_basic_set_involves_dims(
1332 __isl_keep isl_basic_set *bset,
1333 enum isl_dim_type type, unsigned first, unsigned n);
1334 int isl_set_involves_dims(__isl_keep isl_set *set,
1335 enum isl_dim_type type, unsigned first, unsigned n);
1336 int isl_basic_map_involves_dims(
1337 __isl_keep isl_basic_map *bmap,
1338 enum isl_dim_type type, unsigned first, unsigned n);
1339 int isl_map_involves_dims(__isl_keep isl_map *map,
1340 enum isl_dim_type type, unsigned first, unsigned n);
1342 Similarly, the following functions can be used to check whether
1343 a given dimension is involved in any lower or upper bound.
1345 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1346 enum isl_dim_type type, unsigned pos);
1347 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1348 enum isl_dim_type type, unsigned pos);
1350 The identifiers or names of the domain and range spaces of a set
1351 or relation can be read off or set using the following functions.
1353 __isl_give isl_set *isl_set_set_tuple_id(
1354 __isl_take isl_set *set, __isl_take isl_id *id);
1355 __isl_give isl_set *isl_set_reset_tuple_id(
1356 __isl_take isl_set *set);
1357 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1358 __isl_give isl_id *isl_set_get_tuple_id(
1359 __isl_keep isl_set *set);
1360 __isl_give isl_map *isl_map_set_tuple_id(
1361 __isl_take isl_map *map, enum isl_dim_type type,
1362 __isl_take isl_id *id);
1363 __isl_give isl_map *isl_map_reset_tuple_id(
1364 __isl_take isl_map *map, enum isl_dim_type type);
1365 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1366 enum isl_dim_type type);
1367 __isl_give isl_id *isl_map_get_tuple_id(
1368 __isl_keep isl_map *map, enum isl_dim_type type);
1370 const char *isl_basic_set_get_tuple_name(
1371 __isl_keep isl_basic_set *bset);
1372 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1373 __isl_take isl_basic_set *set, const char *s);
1374 const char *isl_set_get_tuple_name(
1375 __isl_keep isl_set *set);
1376 const char *isl_basic_map_get_tuple_name(
1377 __isl_keep isl_basic_map *bmap,
1378 enum isl_dim_type type);
1379 const char *isl_map_get_tuple_name(
1380 __isl_keep isl_map *map,
1381 enum isl_dim_type type);
1383 As with C<isl_dim_get_tuple_name>, the value returned points to
1384 an internal data structure.
1385 The identifiers, positions or names of individual dimensions can be
1386 read off using the following functions.
1388 __isl_give isl_set *isl_set_set_dim_id(
1389 __isl_take isl_set *set, enum isl_dim_type type,
1390 unsigned pos, __isl_take isl_id *id);
1391 int isl_set_has_dim_id(__isl_keep isl_set *set,
1392 enum isl_dim_type type, unsigned pos);
1393 __isl_give isl_id *isl_set_get_dim_id(
1394 __isl_keep isl_set *set, enum isl_dim_type type,
1396 __isl_give isl_map *isl_map_set_dim_id(
1397 __isl_take isl_map *map, enum isl_dim_type type,
1398 unsigned pos, __isl_take isl_id *id);
1399 int isl_map_has_dim_id(__isl_keep isl_map *map,
1400 enum isl_dim_type type, unsigned pos);
1401 __isl_give isl_id *isl_map_get_dim_id(
1402 __isl_keep isl_map *map, enum isl_dim_type type,
1405 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1406 enum isl_dim_type type, __isl_keep isl_id *id);
1407 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1408 enum isl_dim_type type, __isl_keep isl_id *id);
1410 const char *isl_constraint_get_dim_name(
1411 __isl_keep isl_constraint *constraint,
1412 enum isl_dim_type type, unsigned pos);
1413 const char *isl_basic_set_get_dim_name(
1414 __isl_keep isl_basic_set *bset,
1415 enum isl_dim_type type, unsigned pos);
1416 const char *isl_set_get_dim_name(
1417 __isl_keep isl_set *set,
1418 enum isl_dim_type type, unsigned pos);
1419 const char *isl_basic_map_get_dim_name(
1420 __isl_keep isl_basic_map *bmap,
1421 enum isl_dim_type type, unsigned pos);
1422 const char *isl_map_get_dim_name(
1423 __isl_keep isl_map *map,
1424 enum isl_dim_type type, unsigned pos);
1426 These functions are mostly useful to obtain the identifiers, positions
1427 or names of the parameters. Identifiers of individual dimensions are
1428 essentially only useful for printing. They are ignored by all other
1429 operations and may not be preserved across those operations.
1433 =head3 Unary Properties
1439 The following functions test whether the given set or relation
1440 contains any integer points. The ``plain'' variants do not perform
1441 any computations, but simply check if the given set or relation
1442 is already known to be empty.
1444 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1445 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1446 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1447 int isl_set_is_empty(__isl_keep isl_set *set);
1448 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1449 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1450 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1451 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1452 int isl_map_is_empty(__isl_keep isl_map *map);
1453 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1455 =item * Universality
1457 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1458 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1459 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1461 =item * Single-valuedness
1463 int isl_map_is_single_valued(__isl_keep isl_map *map);
1464 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1468 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1469 int isl_map_is_injective(__isl_keep isl_map *map);
1470 int isl_union_map_plain_is_injective(
1471 __isl_keep isl_union_map *umap);
1472 int isl_union_map_is_injective(
1473 __isl_keep isl_union_map *umap);
1477 int isl_map_is_bijective(__isl_keep isl_map *map);
1478 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1482 int isl_basic_map_plain_is_fixed(
1483 __isl_keep isl_basic_map *bmap,
1484 enum isl_dim_type type, unsigned pos,
1486 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1487 enum isl_dim_type type, unsigned pos,
1490 Check if the relation obviously lies on a hyperplane where the given dimension
1491 has a fixed value and if so, return that value in C<*val>.
1495 The following functions check whether the domain of the given
1496 (basic) set is a wrapped relation.
1498 int isl_basic_set_is_wrapping(
1499 __isl_keep isl_basic_set *bset);
1500 int isl_set_is_wrapping(__isl_keep isl_set *set);
1502 =item * Internal Product
1504 int isl_basic_map_can_zip(
1505 __isl_keep isl_basic_map *bmap);
1506 int isl_map_can_zip(__isl_keep isl_map *map);
1508 Check whether the product of domain and range of the given relation
1510 i.e., whether both domain and range are nested relations.
1514 =head3 Binary Properties
1520 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1521 __isl_keep isl_set *set2);
1522 int isl_set_is_equal(__isl_keep isl_set *set1,
1523 __isl_keep isl_set *set2);
1524 int isl_union_set_is_equal(
1525 __isl_keep isl_union_set *uset1,
1526 __isl_keep isl_union_set *uset2);
1527 int isl_basic_map_is_equal(
1528 __isl_keep isl_basic_map *bmap1,
1529 __isl_keep isl_basic_map *bmap2);
1530 int isl_map_is_equal(__isl_keep isl_map *map1,
1531 __isl_keep isl_map *map2);
1532 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1533 __isl_keep isl_map *map2);
1534 int isl_union_map_is_equal(
1535 __isl_keep isl_union_map *umap1,
1536 __isl_keep isl_union_map *umap2);
1538 =item * Disjointness
1540 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1541 __isl_keep isl_set *set2);
1545 int isl_set_is_subset(__isl_keep isl_set *set1,
1546 __isl_keep isl_set *set2);
1547 int isl_set_is_strict_subset(
1548 __isl_keep isl_set *set1,
1549 __isl_keep isl_set *set2);
1550 int isl_union_set_is_subset(
1551 __isl_keep isl_union_set *uset1,
1552 __isl_keep isl_union_set *uset2);
1553 int isl_union_set_is_strict_subset(
1554 __isl_keep isl_union_set *uset1,
1555 __isl_keep isl_union_set *uset2);
1556 int isl_basic_map_is_subset(
1557 __isl_keep isl_basic_map *bmap1,
1558 __isl_keep isl_basic_map *bmap2);
1559 int isl_basic_map_is_strict_subset(
1560 __isl_keep isl_basic_map *bmap1,
1561 __isl_keep isl_basic_map *bmap2);
1562 int isl_map_is_subset(
1563 __isl_keep isl_map *map1,
1564 __isl_keep isl_map *map2);
1565 int isl_map_is_strict_subset(
1566 __isl_keep isl_map *map1,
1567 __isl_keep isl_map *map2);
1568 int isl_union_map_is_subset(
1569 __isl_keep isl_union_map *umap1,
1570 __isl_keep isl_union_map *umap2);
1571 int isl_union_map_is_strict_subset(
1572 __isl_keep isl_union_map *umap1,
1573 __isl_keep isl_union_map *umap2);
1577 =head2 Unary Operations
1583 __isl_give isl_set *isl_set_complement(
1584 __isl_take isl_set *set);
1588 __isl_give isl_basic_map *isl_basic_map_reverse(
1589 __isl_take isl_basic_map *bmap);
1590 __isl_give isl_map *isl_map_reverse(
1591 __isl_take isl_map *map);
1592 __isl_give isl_union_map *isl_union_map_reverse(
1593 __isl_take isl_union_map *umap);
1597 __isl_give isl_basic_set *isl_basic_set_project_out(
1598 __isl_take isl_basic_set *bset,
1599 enum isl_dim_type type, unsigned first, unsigned n);
1600 __isl_give isl_basic_map *isl_basic_map_project_out(
1601 __isl_take isl_basic_map *bmap,
1602 enum isl_dim_type type, unsigned first, unsigned n);
1603 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1604 enum isl_dim_type type, unsigned first, unsigned n);
1605 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1606 enum isl_dim_type type, unsigned first, unsigned n);
1607 __isl_give isl_basic_set *isl_basic_map_domain(
1608 __isl_take isl_basic_map *bmap);
1609 __isl_give isl_basic_set *isl_basic_map_range(
1610 __isl_take isl_basic_map *bmap);
1611 __isl_give isl_set *isl_map_domain(
1612 __isl_take isl_map *bmap);
1613 __isl_give isl_set *isl_map_range(
1614 __isl_take isl_map *map);
1615 __isl_give isl_union_set *isl_union_map_domain(
1616 __isl_take isl_union_map *umap);
1617 __isl_give isl_union_set *isl_union_map_range(
1618 __isl_take isl_union_map *umap);
1620 __isl_give isl_basic_map *isl_basic_map_domain_map(
1621 __isl_take isl_basic_map *bmap);
1622 __isl_give isl_basic_map *isl_basic_map_range_map(
1623 __isl_take isl_basic_map *bmap);
1624 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1625 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1626 __isl_give isl_union_map *isl_union_map_domain_map(
1627 __isl_take isl_union_map *umap);
1628 __isl_give isl_union_map *isl_union_map_range_map(
1629 __isl_take isl_union_map *umap);
1631 The functions above construct a (basic, regular or union) relation
1632 that maps (a wrapped version of) the input relation to its domain or range.
1636 __isl_give isl_set *isl_set_eliminate(
1637 __isl_take isl_set *set, enum isl_dim_type type,
1638 unsigned first, unsigned n);
1640 Eliminate the coefficients for the given dimensions from the constraints,
1641 without removing the dimensions.
1645 __isl_give isl_basic_set *isl_basic_set_fix(
1646 __isl_take isl_basic_set *bset,
1647 enum isl_dim_type type, unsigned pos,
1649 __isl_give isl_basic_set *isl_basic_set_fix_si(
1650 __isl_take isl_basic_set *bset,
1651 enum isl_dim_type type, unsigned pos, int value);
1652 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1653 enum isl_dim_type type, unsigned pos,
1655 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1656 enum isl_dim_type type, unsigned pos, int value);
1657 __isl_give isl_basic_map *isl_basic_map_fix_si(
1658 __isl_take isl_basic_map *bmap,
1659 enum isl_dim_type type, unsigned pos, int value);
1660 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1661 enum isl_dim_type type, unsigned pos, int value);
1663 Intersect the set or relation with the hyperplane where the given
1664 dimension has the fixed given value.
1666 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1667 enum isl_dim_type type1, int pos1,
1668 enum isl_dim_type type2, int pos2);
1669 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1670 enum isl_dim_type type1, int pos1,
1671 enum isl_dim_type type2, int pos2);
1673 Intersect the set or relation with the hyperplane where the given
1674 dimensions are equal to each other.
1676 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1677 enum isl_dim_type type1, int pos1,
1678 enum isl_dim_type type2, int pos2);
1680 Intersect the relation with the hyperplane where the given
1681 dimensions have opposite values.
1685 __isl_give isl_map *isl_set_identity(
1686 __isl_take isl_set *set);
1687 __isl_give isl_union_map *isl_union_set_identity(
1688 __isl_take isl_union_set *uset);
1690 Construct an identity relation on the given (union) set.
1694 __isl_give isl_basic_set *isl_basic_map_deltas(
1695 __isl_take isl_basic_map *bmap);
1696 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1697 __isl_give isl_union_set *isl_union_map_deltas(
1698 __isl_take isl_union_map *umap);
1700 These functions return a (basic) set containing the differences
1701 between image elements and corresponding domain elements in the input.
1703 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1704 __isl_take isl_basic_map *bmap);
1705 __isl_give isl_map *isl_map_deltas_map(
1706 __isl_take isl_map *map);
1707 __isl_give isl_union_map *isl_union_map_deltas_map(
1708 __isl_take isl_union_map *umap);
1710 The functions above construct a (basic, regular or union) relation
1711 that maps (a wrapped version of) the input relation to its delta set.
1715 Simplify the representation of a set or relation by trying
1716 to combine pairs of basic sets or relations into a single
1717 basic set or relation.
1719 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1720 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1721 __isl_give isl_union_set *isl_union_set_coalesce(
1722 __isl_take isl_union_set *uset);
1723 __isl_give isl_union_map *isl_union_map_coalesce(
1724 __isl_take isl_union_map *umap);
1726 =item * Detecting equalities
1728 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1729 __isl_take isl_basic_set *bset);
1730 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1731 __isl_take isl_basic_map *bmap);
1732 __isl_give isl_set *isl_set_detect_equalities(
1733 __isl_take isl_set *set);
1734 __isl_give isl_map *isl_map_detect_equalities(
1735 __isl_take isl_map *map);
1736 __isl_give isl_union_set *isl_union_set_detect_equalities(
1737 __isl_take isl_union_set *uset);
1738 __isl_give isl_union_map *isl_union_map_detect_equalities(
1739 __isl_take isl_union_map *umap);
1741 Simplify the representation of a set or relation by detecting implicit
1744 =item * Removing redundant constraints
1746 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1747 __isl_take isl_basic_set *bset);
1748 __isl_give isl_set *isl_set_remove_redundancies(
1749 __isl_take isl_set *set);
1750 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1751 __isl_take isl_basic_map *bmap);
1752 __isl_give isl_map *isl_map_remove_redundancies(
1753 __isl_take isl_map *map);
1757 __isl_give isl_basic_set *isl_set_convex_hull(
1758 __isl_take isl_set *set);
1759 __isl_give isl_basic_map *isl_map_convex_hull(
1760 __isl_take isl_map *map);
1762 If the input set or relation has any existentially quantified
1763 variables, then the result of these operations is currently undefined.
1767 __isl_give isl_basic_set *isl_set_simple_hull(
1768 __isl_take isl_set *set);
1769 __isl_give isl_basic_map *isl_map_simple_hull(
1770 __isl_take isl_map *map);
1771 __isl_give isl_union_map *isl_union_map_simple_hull(
1772 __isl_take isl_union_map *umap);
1774 These functions compute a single basic set or relation
1775 that contains the whole input set or relation.
1776 In particular, the output is described by translates
1777 of the constraints describing the basic sets or relations in the input.
1781 (See \autoref{s:simple hull}.)
1787 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1788 __isl_take isl_basic_set *bset);
1789 __isl_give isl_basic_set *isl_set_affine_hull(
1790 __isl_take isl_set *set);
1791 __isl_give isl_union_set *isl_union_set_affine_hull(
1792 __isl_take isl_union_set *uset);
1793 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1794 __isl_take isl_basic_map *bmap);
1795 __isl_give isl_basic_map *isl_map_affine_hull(
1796 __isl_take isl_map *map);
1797 __isl_give isl_union_map *isl_union_map_affine_hull(
1798 __isl_take isl_union_map *umap);
1800 In case of union sets and relations, the affine hull is computed
1803 =item * Polyhedral hull
1805 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1806 __isl_take isl_set *set);
1807 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1808 __isl_take isl_map *map);
1809 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1810 __isl_take isl_union_set *uset);
1811 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1812 __isl_take isl_union_map *umap);
1814 These functions compute a single basic set or relation
1815 not involving any existentially quantified variables
1816 that contains the whole input set or relation.
1817 In case of union sets and relations, the polyhedral hull is computed
1820 =item * Optimization
1822 #include <isl/ilp.h>
1823 enum isl_lp_result isl_basic_set_max(
1824 __isl_keep isl_basic_set *bset,
1825 __isl_keep isl_aff *obj, isl_int *opt)
1826 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1827 __isl_keep isl_aff *obj, isl_int *opt);
1828 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1829 __isl_keep isl_aff *obj, isl_int *opt);
1831 Compute the minimum or maximum of the integer affine expression C<obj>
1832 over the points in C<set>, returning the result in C<opt>.
1833 The return value may be one of C<isl_lp_error>,
1834 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1836 =item * Parametric optimization
1838 __isl_give isl_pw_aff *isl_set_dim_min(
1839 __isl_take isl_set *set, int pos);
1840 __isl_give isl_pw_aff *isl_set_dim_max(
1841 __isl_take isl_set *set, int pos);
1843 Compute the minimum or maximum of the given set dimension as a function of the
1844 parameters, but independently of the other set dimensions.
1845 For lexicographic optimization, see L<"Lexicographic Optimization">.
1849 The following functions compute either the set of (rational) coefficient
1850 values of valid constraints for the given set or the set of (rational)
1851 values satisfying the constraints with coefficients from the given set.
1852 Internally, these two sets of functions perform essentially the
1853 same operations, except that the set of coefficients is assumed to
1854 be a cone, while the set of values may be any polyhedron.
1855 The current implementation is based on the Farkas lemma and
1856 Fourier-Motzkin elimination, but this may change or be made optional
1857 in future. In particular, future implementations may use different
1858 dualization algorithms or skip the elimination step.
1860 __isl_give isl_basic_set *isl_basic_set_coefficients(
1861 __isl_take isl_basic_set *bset);
1862 __isl_give isl_basic_set *isl_set_coefficients(
1863 __isl_take isl_set *set);
1864 __isl_give isl_union_set *isl_union_set_coefficients(
1865 __isl_take isl_union_set *bset);
1866 __isl_give isl_basic_set *isl_basic_set_solutions(
1867 __isl_take isl_basic_set *bset);
1868 __isl_give isl_basic_set *isl_set_solutions(
1869 __isl_take isl_set *set);
1870 __isl_give isl_union_set *isl_union_set_solutions(
1871 __isl_take isl_union_set *bset);
1875 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1877 __isl_give isl_union_map *isl_union_map_power(
1878 __isl_take isl_union_map *umap, int *exact);
1880 Compute a parametric representation for all positive powers I<k> of C<map>.
1881 The result maps I<k> to a nested relation corresponding to the
1882 I<k>th power of C<map>.
1883 The result may be an overapproximation. If the result is known to be exact,
1884 then C<*exact> is set to C<1>.
1886 =item * Transitive closure
1888 __isl_give isl_map *isl_map_transitive_closure(
1889 __isl_take isl_map *map, int *exact);
1890 __isl_give isl_union_map *isl_union_map_transitive_closure(
1891 __isl_take isl_union_map *umap, int *exact);
1893 Compute the transitive closure 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 * Reaching path lengths
1899 __isl_give isl_map *isl_map_reaching_path_lengths(
1900 __isl_take isl_map *map, int *exact);
1902 Compute a relation that maps each element in the range of C<map>
1903 to the lengths of all paths composed of edges in C<map> that
1904 end up in the given element.
1905 The result may be an overapproximation. If the result is known to be exact,
1906 then C<*exact> is set to C<1>.
1907 To compute the I<maximal> path length, the resulting relation
1908 should be postprocessed by C<isl_map_lexmax>.
1909 In particular, if the input relation is a dependence relation
1910 (mapping sources to sinks), then the maximal path length corresponds
1911 to the free schedule.
1912 Note, however, that C<isl_map_lexmax> expects the maximum to be
1913 finite, so if the path lengths are unbounded (possibly due to
1914 the overapproximation), then you will get an error message.
1918 __isl_give isl_basic_set *isl_basic_map_wrap(
1919 __isl_take isl_basic_map *bmap);
1920 __isl_give isl_set *isl_map_wrap(
1921 __isl_take isl_map *map);
1922 __isl_give isl_union_set *isl_union_map_wrap(
1923 __isl_take isl_union_map *umap);
1924 __isl_give isl_basic_map *isl_basic_set_unwrap(
1925 __isl_take isl_basic_set *bset);
1926 __isl_give isl_map *isl_set_unwrap(
1927 __isl_take isl_set *set);
1928 __isl_give isl_union_map *isl_union_set_unwrap(
1929 __isl_take isl_union_set *uset);
1933 Remove any internal structure of domain (and range) of the given
1934 set or relation. If there is any such internal structure in the input,
1935 then the name of the space is also removed.
1937 __isl_give isl_basic_set *isl_basic_set_flatten(
1938 __isl_take isl_basic_set *bset);
1939 __isl_give isl_set *isl_set_flatten(
1940 __isl_take isl_set *set);
1941 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1942 __isl_take isl_basic_map *bmap);
1943 __isl_give isl_map *isl_map_flatten_range(
1944 __isl_take isl_map *map);
1945 __isl_give isl_basic_map *isl_basic_map_flatten(
1946 __isl_take isl_basic_map *bmap);
1947 __isl_give isl_map *isl_map_flatten(
1948 __isl_take isl_map *map);
1950 __isl_give isl_map *isl_set_flatten_map(
1951 __isl_take isl_set *set);
1953 The function above constructs a relation
1954 that maps the input set to a flattened version of the set.
1958 Lift the input set to a space with extra dimensions corresponding
1959 to the existentially quantified variables in the input.
1960 In particular, the result lives in a wrapped map where the domain
1961 is the original space and the range corresponds to the original
1962 existentially quantified variables.
1964 __isl_give isl_basic_set *isl_basic_set_lift(
1965 __isl_take isl_basic_set *bset);
1966 __isl_give isl_set *isl_set_lift(
1967 __isl_take isl_set *set);
1968 __isl_give isl_union_set *isl_union_set_lift(
1969 __isl_take isl_union_set *uset);
1971 =item * Internal Product
1973 __isl_give isl_basic_map *isl_basic_map_zip(
1974 __isl_take isl_basic_map *bmap);
1975 __isl_give isl_map *isl_map_zip(
1976 __isl_take isl_map *map);
1977 __isl_give isl_union_map *isl_union_map_zip(
1978 __isl_take isl_union_map *umap);
1980 Given a relation with nested relations for domain and range,
1981 interchange the range of the domain with the domain of the range.
1983 =item * Aligning parameters
1985 __isl_give isl_set *isl_set_align_params(
1986 __isl_take isl_set *set,
1987 __isl_take isl_dim *model);
1988 __isl_give isl_map *isl_map_align_params(
1989 __isl_take isl_map *map,
1990 __isl_take isl_dim *model);
1992 Change the order of the parameters of the given set or relation
1993 such that the first parameters match those of C<model>.
1994 This may involve the introduction of extra parameters.
1995 All parameters need to be named.
1997 =item * Dimension manipulation
1999 __isl_give isl_set *isl_set_add_dims(
2000 __isl_take isl_set *set,
2001 enum isl_dim_type type, unsigned n);
2002 __isl_give isl_map *isl_map_add_dims(
2003 __isl_take isl_map *map,
2004 enum isl_dim_type type, unsigned n);
2005 __isl_give isl_set *isl_set_insert_dims(
2006 __isl_take isl_set *set,
2007 enum isl_dim_type type, unsigned pos, unsigned n);
2008 __isl_give isl_map *isl_map_insert_dims(
2009 __isl_take isl_map *map,
2010 enum isl_dim_type type, unsigned pos, unsigned n);
2012 It is usually not advisable to directly change the (input or output)
2013 space of a set or a relation as this removes the name and the internal
2014 structure of the space. However, the above functions can be useful
2015 to add new parameters, assuming
2016 C<isl_set_align_params> and C<isl_map_align_params>
2021 =head2 Binary Operations
2023 The two arguments of a binary operation not only need to live
2024 in the same C<isl_ctx>, they currently also need to have
2025 the same (number of) parameters.
2027 =head3 Basic Operations
2031 =item * Intersection
2033 __isl_give isl_basic_set *isl_basic_set_intersect(
2034 __isl_take isl_basic_set *bset1,
2035 __isl_take isl_basic_set *bset2);
2036 __isl_give isl_set *isl_set_intersect_params(
2037 __isl_take isl_set *set,
2038 __isl_take isl_set *params);
2039 __isl_give isl_set *isl_set_intersect(
2040 __isl_take isl_set *set1,
2041 __isl_take isl_set *set2);
2042 __isl_give isl_union_set *isl_union_set_intersect(
2043 __isl_take isl_union_set *uset1,
2044 __isl_take isl_union_set *uset2);
2045 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2046 __isl_take isl_basic_map *bmap,
2047 __isl_take isl_basic_set *bset);
2048 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2049 __isl_take isl_basic_map *bmap,
2050 __isl_take isl_basic_set *bset);
2051 __isl_give isl_basic_map *isl_basic_map_intersect(
2052 __isl_take isl_basic_map *bmap1,
2053 __isl_take isl_basic_map *bmap2);
2054 __isl_give isl_map *isl_map_intersect_params(
2055 __isl_take isl_map *map,
2056 __isl_take isl_set *params);
2057 __isl_give isl_map *isl_map_intersect_domain(
2058 __isl_take isl_map *map,
2059 __isl_take isl_set *set);
2060 __isl_give isl_map *isl_map_intersect_range(
2061 __isl_take isl_map *map,
2062 __isl_take isl_set *set);
2063 __isl_give isl_map *isl_map_intersect(
2064 __isl_take isl_map *map1,
2065 __isl_take isl_map *map2);
2066 __isl_give isl_union_map *isl_union_map_intersect_domain(
2067 __isl_take isl_union_map *umap,
2068 __isl_take isl_union_set *uset);
2069 __isl_give isl_union_map *isl_union_map_intersect_range(
2070 __isl_take isl_union_map *umap,
2071 __isl_take isl_union_set *uset);
2072 __isl_give isl_union_map *isl_union_map_intersect(
2073 __isl_take isl_union_map *umap1,
2074 __isl_take isl_union_map *umap2);
2078 __isl_give isl_set *isl_basic_set_union(
2079 __isl_take isl_basic_set *bset1,
2080 __isl_take isl_basic_set *bset2);
2081 __isl_give isl_map *isl_basic_map_union(
2082 __isl_take isl_basic_map *bmap1,
2083 __isl_take isl_basic_map *bmap2);
2084 __isl_give isl_set *isl_set_union(
2085 __isl_take isl_set *set1,
2086 __isl_take isl_set *set2);
2087 __isl_give isl_map *isl_map_union(
2088 __isl_take isl_map *map1,
2089 __isl_take isl_map *map2);
2090 __isl_give isl_union_set *isl_union_set_union(
2091 __isl_take isl_union_set *uset1,
2092 __isl_take isl_union_set *uset2);
2093 __isl_give isl_union_map *isl_union_map_union(
2094 __isl_take isl_union_map *umap1,
2095 __isl_take isl_union_map *umap2);
2097 =item * Set difference
2099 __isl_give isl_set *isl_set_subtract(
2100 __isl_take isl_set *set1,
2101 __isl_take isl_set *set2);
2102 __isl_give isl_map *isl_map_subtract(
2103 __isl_take isl_map *map1,
2104 __isl_take isl_map *map2);
2105 __isl_give isl_union_set *isl_union_set_subtract(
2106 __isl_take isl_union_set *uset1,
2107 __isl_take isl_union_set *uset2);
2108 __isl_give isl_union_map *isl_union_map_subtract(
2109 __isl_take isl_union_map *umap1,
2110 __isl_take isl_union_map *umap2);
2114 __isl_give isl_basic_set *isl_basic_set_apply(
2115 __isl_take isl_basic_set *bset,
2116 __isl_take isl_basic_map *bmap);
2117 __isl_give isl_set *isl_set_apply(
2118 __isl_take isl_set *set,
2119 __isl_take isl_map *map);
2120 __isl_give isl_union_set *isl_union_set_apply(
2121 __isl_take isl_union_set *uset,
2122 __isl_take isl_union_map *umap);
2123 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2124 __isl_take isl_basic_map *bmap1,
2125 __isl_take isl_basic_map *bmap2);
2126 __isl_give isl_basic_map *isl_basic_map_apply_range(
2127 __isl_take isl_basic_map *bmap1,
2128 __isl_take isl_basic_map *bmap2);
2129 __isl_give isl_map *isl_map_apply_domain(
2130 __isl_take isl_map *map1,
2131 __isl_take isl_map *map2);
2132 __isl_give isl_union_map *isl_union_map_apply_domain(
2133 __isl_take isl_union_map *umap1,
2134 __isl_take isl_union_map *umap2);
2135 __isl_give isl_map *isl_map_apply_range(
2136 __isl_take isl_map *map1,
2137 __isl_take isl_map *map2);
2138 __isl_give isl_union_map *isl_union_map_apply_range(
2139 __isl_take isl_union_map *umap1,
2140 __isl_take isl_union_map *umap2);
2142 =item * Cartesian Product
2144 __isl_give isl_set *isl_set_product(
2145 __isl_take isl_set *set1,
2146 __isl_take isl_set *set2);
2147 __isl_give isl_union_set *isl_union_set_product(
2148 __isl_take isl_union_set *uset1,
2149 __isl_take isl_union_set *uset2);
2150 __isl_give isl_basic_map *isl_basic_map_range_product(
2151 __isl_take isl_basic_map *bmap1,
2152 __isl_take isl_basic_map *bmap2);
2153 __isl_give isl_map *isl_map_range_product(
2154 __isl_take isl_map *map1,
2155 __isl_take isl_map *map2);
2156 __isl_give isl_union_map *isl_union_map_range_product(
2157 __isl_take isl_union_map *umap1,
2158 __isl_take isl_union_map *umap2);
2159 __isl_give isl_map *isl_map_product(
2160 __isl_take isl_map *map1,
2161 __isl_take isl_map *map2);
2162 __isl_give isl_union_map *isl_union_map_product(
2163 __isl_take isl_union_map *umap1,
2164 __isl_take isl_union_map *umap2);
2166 The above functions compute the cross product of the given
2167 sets or relations. The domains and ranges of the results
2168 are wrapped maps between domains and ranges of the inputs.
2169 To obtain a ``flat'' product, use the following functions
2172 __isl_give isl_basic_set *isl_basic_set_flat_product(
2173 __isl_take isl_basic_set *bset1,
2174 __isl_take isl_basic_set *bset2);
2175 __isl_give isl_set *isl_set_flat_product(
2176 __isl_take isl_set *set1,
2177 __isl_take isl_set *set2);
2178 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2179 __isl_take isl_basic_map *bmap1,
2180 __isl_take isl_basic_map *bmap2);
2181 __isl_give isl_map *isl_map_flat_range_product(
2182 __isl_take isl_map *map1,
2183 __isl_take isl_map *map2);
2184 __isl_give isl_union_map *isl_union_map_flat_range_product(
2185 __isl_take isl_union_map *umap1,
2186 __isl_take isl_union_map *umap2);
2187 __isl_give isl_basic_map *isl_basic_map_flat_product(
2188 __isl_take isl_basic_map *bmap1,
2189 __isl_take isl_basic_map *bmap2);
2190 __isl_give isl_map *isl_map_flat_product(
2191 __isl_take isl_map *map1,
2192 __isl_take isl_map *map2);
2194 =item * Simplification
2196 __isl_give isl_basic_set *isl_basic_set_gist(
2197 __isl_take isl_basic_set *bset,
2198 __isl_take isl_basic_set *context);
2199 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2200 __isl_take isl_set *context);
2201 __isl_give isl_union_set *isl_union_set_gist(
2202 __isl_take isl_union_set *uset,
2203 __isl_take isl_union_set *context);
2204 __isl_give isl_basic_map *isl_basic_map_gist(
2205 __isl_take isl_basic_map *bmap,
2206 __isl_take isl_basic_map *context);
2207 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2208 __isl_take isl_map *context);
2209 __isl_give isl_union_map *isl_union_map_gist(
2210 __isl_take isl_union_map *umap,
2211 __isl_take isl_union_map *context);
2213 The gist operation returns a set or relation that has the
2214 same intersection with the context as the input set or relation.
2215 Any implicit equality in the intersection is made explicit in the result,
2216 while all inequalities that are redundant with respect to the intersection
2218 In case of union sets and relations, the gist operation is performed
2223 =head3 Lexicographic Optimization
2225 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2226 the following functions
2227 compute a set that contains the lexicographic minimum or maximum
2228 of the elements in C<set> (or C<bset>) for those values of the parameters
2229 that satisfy C<dom>.
2230 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2231 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2233 In other words, the union of the parameter values
2234 for which the result is non-empty and of C<*empty>
2237 __isl_give isl_set *isl_basic_set_partial_lexmin(
2238 __isl_take isl_basic_set *bset,
2239 __isl_take isl_basic_set *dom,
2240 __isl_give isl_set **empty);
2241 __isl_give isl_set *isl_basic_set_partial_lexmax(
2242 __isl_take isl_basic_set *bset,
2243 __isl_take isl_basic_set *dom,
2244 __isl_give isl_set **empty);
2245 __isl_give isl_set *isl_set_partial_lexmin(
2246 __isl_take isl_set *set, __isl_take isl_set *dom,
2247 __isl_give isl_set **empty);
2248 __isl_give isl_set *isl_set_partial_lexmax(
2249 __isl_take isl_set *set, __isl_take isl_set *dom,
2250 __isl_give isl_set **empty);
2252 Given a (basic) set C<set> (or C<bset>), the following functions simply
2253 return a set containing the lexicographic minimum or maximum
2254 of the elements in C<set> (or C<bset>).
2255 In case of union sets, the optimum is computed per space.
2257 __isl_give isl_set *isl_basic_set_lexmin(
2258 __isl_take isl_basic_set *bset);
2259 __isl_give isl_set *isl_basic_set_lexmax(
2260 __isl_take isl_basic_set *bset);
2261 __isl_give isl_set *isl_set_lexmin(
2262 __isl_take isl_set *set);
2263 __isl_give isl_set *isl_set_lexmax(
2264 __isl_take isl_set *set);
2265 __isl_give isl_union_set *isl_union_set_lexmin(
2266 __isl_take isl_union_set *uset);
2267 __isl_give isl_union_set *isl_union_set_lexmax(
2268 __isl_take isl_union_set *uset);
2270 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2271 the following functions
2272 compute a relation that maps each element of C<dom>
2273 to the single lexicographic minimum or maximum
2274 of the elements that are associated to that same
2275 element in C<map> (or C<bmap>).
2276 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2277 that contains the elements in C<dom> that do not map
2278 to any elements in C<map> (or C<bmap>).
2279 In other words, the union of the domain of the result and of C<*empty>
2282 __isl_give isl_map *isl_basic_map_partial_lexmax(
2283 __isl_take isl_basic_map *bmap,
2284 __isl_take isl_basic_set *dom,
2285 __isl_give isl_set **empty);
2286 __isl_give isl_map *isl_basic_map_partial_lexmin(
2287 __isl_take isl_basic_map *bmap,
2288 __isl_take isl_basic_set *dom,
2289 __isl_give isl_set **empty);
2290 __isl_give isl_map *isl_map_partial_lexmax(
2291 __isl_take isl_map *map, __isl_take isl_set *dom,
2292 __isl_give isl_set **empty);
2293 __isl_give isl_map *isl_map_partial_lexmin(
2294 __isl_take isl_map *map, __isl_take isl_set *dom,
2295 __isl_give isl_set **empty);
2297 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2298 return a map mapping each element in the domain of
2299 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2300 of all elements associated to that element.
2301 In case of union relations, the optimum is computed per space.
2303 __isl_give isl_map *isl_basic_map_lexmin(
2304 __isl_take isl_basic_map *bmap);
2305 __isl_give isl_map *isl_basic_map_lexmax(
2306 __isl_take isl_basic_map *bmap);
2307 __isl_give isl_map *isl_map_lexmin(
2308 __isl_take isl_map *map);
2309 __isl_give isl_map *isl_map_lexmax(
2310 __isl_take isl_map *map);
2311 __isl_give isl_union_map *isl_union_map_lexmin(
2312 __isl_take isl_union_map *umap);
2313 __isl_give isl_union_map *isl_union_map_lexmax(
2314 __isl_take isl_union_map *umap);
2318 Lists are defined over several element types, including
2319 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2320 Here we take lists of C<isl_set>s as an example.
2321 Lists can be created, copied and freed using the following functions.
2323 #include <isl/list.h>
2324 __isl_give isl_set_list *isl_set_list_from_set(
2325 __isl_take isl_set *el);
2326 __isl_give isl_set_list *isl_set_list_alloc(
2327 isl_ctx *ctx, int n);
2328 __isl_give isl_set_list *isl_set_list_copy(
2329 __isl_keep isl_set_list *list);
2330 __isl_give isl_set_list *isl_set_list_add(
2331 __isl_take isl_set_list *list,
2332 __isl_take isl_set *el);
2333 __isl_give isl_set_list *isl_set_list_concat(
2334 __isl_take isl_set_list *list1,
2335 __isl_take isl_set_list *list2);
2336 void *isl_set_list_free(__isl_take isl_set_list *list);
2338 C<isl_set_list_alloc> creates an empty list with a capacity for
2339 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2342 Lists can be inspected using the following functions.
2344 #include <isl/list.h>
2345 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2346 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2347 __isl_give isl_set *isl_set_list_get_set(
2348 __isl_keep isl_set_list *list, int index);
2349 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2350 int (*fn)(__isl_take isl_set *el, void *user),
2353 Lists can be printed using
2355 #include <isl/list.h>
2356 __isl_give isl_printer *isl_printer_print_set_list(
2357 __isl_take isl_printer *p,
2358 __isl_keep isl_set_list *list);
2362 Matrices can be created, copied and freed using the following functions.
2364 #include <isl/mat.h>
2365 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2366 unsigned n_row, unsigned n_col);
2367 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2368 void isl_mat_free(__isl_take isl_mat *mat);
2370 Note that the elements of a newly created matrix may have arbitrary values.
2371 The elements can be changed and inspected using the following functions.
2373 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2374 int isl_mat_rows(__isl_keep isl_mat *mat);
2375 int isl_mat_cols(__isl_keep isl_mat *mat);
2376 int isl_mat_get_element(__isl_keep isl_mat *mat,
2377 int row, int col, isl_int *v);
2378 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2379 int row, int col, isl_int v);
2380 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2381 int row, int col, int v);
2383 C<isl_mat_get_element> will return a negative value if anything went wrong.
2384 In that case, the value of C<*v> is undefined.
2386 The following function can be used to compute the (right) inverse
2387 of a matrix, i.e., a matrix such that the product of the original
2388 and the inverse (in that order) is a multiple of the identity matrix.
2389 The input matrix is assumed to be of full row-rank.
2391 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2393 The following function can be used to compute the (right) kernel
2394 (or null space) of a matrix, i.e., a matrix such that the product of
2395 the original and the kernel (in that order) is the zero matrix.
2397 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2399 =head2 Piecewise Quasi Affine Expressions
2401 The zero quasi affine expression can be created using
2403 __isl_give isl_aff *isl_aff_zero(
2404 __isl_take isl_local_space *ls);
2406 A quasi affine expression can also be initialized from an C<isl_div>:
2408 #include <isl/div.h>
2409 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2411 An empty piecewise quasi affine expression (one with no cells)
2412 or a piecewise quasi affine expression with a single cell can
2413 be created using the following functions.
2415 #include <isl/aff.h>
2416 __isl_give isl_pw_aff *isl_pw_aff_empty(
2417 __isl_take isl_dim *dim);
2418 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2419 __isl_take isl_set *set, __isl_take isl_aff *aff);
2420 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2421 __isl_take isl_aff *aff);
2423 Quasi affine expressions can be copied and freed using
2425 #include <isl/aff.h>
2426 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2427 void *isl_aff_free(__isl_take isl_aff *aff);
2429 __isl_give isl_pw_aff *isl_pw_aff_copy(
2430 __isl_keep isl_pw_aff *pwaff);
2431 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2433 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2434 using the following function. The constraint is required to have
2435 a non-zero coefficient for the specified dimension.
2437 #include <isl/constraint.h>
2438 __isl_give isl_aff *isl_constraint_get_bound(
2439 __isl_keep isl_constraint *constraint,
2440 enum isl_dim_type type, int pos);
2442 The entire affine expression of the constraint can also be extracted
2443 using the following function.
2445 #include <isl/constraint.h>
2446 __isl_give isl_aff *isl_constraint_get_aff(
2447 __isl_keep isl_constraint *constraint);
2449 Conversely, an equality constraint equating
2450 the affine expression to zero or an inequality constraint enforcing
2451 the affine expression to be non-negative, can be constructed using
2453 __isl_give isl_constraint *isl_equality_from_aff(
2454 __isl_take isl_aff *aff);
2455 __isl_give isl_constraint *isl_inequality_from_aff(
2456 __isl_take isl_aff *aff);
2458 The expression can be inspected using
2460 #include <isl/aff.h>
2461 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2462 int isl_aff_dim(__isl_keep isl_aff *aff,
2463 enum isl_dim_type type);
2464 __isl_give isl_local_space *isl_aff_get_local_space(
2465 __isl_keep isl_aff *aff);
2466 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2467 enum isl_dim_type type, unsigned pos);
2468 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2470 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2471 enum isl_dim_type type, int pos, isl_int *v);
2472 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2474 __isl_give isl_div *isl_aff_get_div(
2475 __isl_keep isl_aff *aff, int pos);
2477 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2478 int (*fn)(__isl_take isl_set *set,
2479 __isl_take isl_aff *aff,
2480 void *user), void *user);
2482 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2483 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2485 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2486 enum isl_dim_type type, unsigned first, unsigned n);
2487 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2488 enum isl_dim_type type, unsigned first, unsigned n);
2490 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2491 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2492 enum isl_dim_type type);
2493 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2495 It can be modified using
2497 #include <isl/aff.h>
2498 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2499 __isl_take isl_pw_aff *pwaff,
2500 __isl_take isl_id *id);
2501 __isl_give isl_aff *isl_aff_set_dim_name(
2502 __isl_take isl_aff *aff, enum isl_dim_type type,
2503 unsigned pos, const char *s);
2504 __isl_give isl_aff *isl_aff_set_constant(
2505 __isl_take isl_aff *aff, isl_int v);
2506 __isl_give isl_aff *isl_aff_set_constant_si(
2507 __isl_take isl_aff *aff, int v);
2508 __isl_give isl_aff *isl_aff_set_coefficient(
2509 __isl_take isl_aff *aff,
2510 enum isl_dim_type type, int pos, isl_int v);
2511 __isl_give isl_aff *isl_aff_set_coefficient_si(
2512 __isl_take isl_aff *aff,
2513 enum isl_dim_type type, int pos, int v);
2514 __isl_give isl_aff *isl_aff_set_denominator(
2515 __isl_take isl_aff *aff, isl_int v);
2517 __isl_give isl_aff *isl_aff_add_constant(
2518 __isl_take isl_aff *aff, isl_int v);
2519 __isl_give isl_aff *isl_aff_add_constant_si(
2520 __isl_take isl_aff *aff, int v);
2521 __isl_give isl_aff *isl_aff_add_coefficient(
2522 __isl_take isl_aff *aff,
2523 enum isl_dim_type type, int pos, isl_int v);
2524 __isl_give isl_aff *isl_aff_add_coefficient_si(
2525 __isl_take isl_aff *aff,
2526 enum isl_dim_type type, int pos, int v);
2528 __isl_give isl_aff *isl_aff_insert_dims(
2529 __isl_take isl_aff *aff,
2530 enum isl_dim_type type, unsigned first, unsigned n);
2531 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2532 __isl_take isl_pw_aff *pwaff,
2533 enum isl_dim_type type, unsigned first, unsigned n);
2534 __isl_give isl_aff *isl_aff_add_dims(
2535 __isl_take isl_aff *aff,
2536 enum isl_dim_type type, unsigned n);
2537 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2538 __isl_take isl_pw_aff *pwaff,
2539 enum isl_dim_type type, unsigned n);
2540 __isl_give isl_aff *isl_aff_drop_dims(
2541 __isl_take isl_aff *aff,
2542 enum isl_dim_type type, unsigned first, unsigned n);
2543 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2544 __isl_take isl_pw_aff *pwaff,
2545 enum isl_dim_type type, unsigned first, unsigned n);
2547 Note that the C<set_constant> and C<set_coefficient> functions
2548 set the I<numerator> of the constant or coefficient, while
2549 C<add_constant> and C<add_coefficient> add an integer value to
2550 the possibly rational constant or coefficient.
2552 To check whether an affine expressions is obviously zero
2553 or obviously equal to some other affine expression, use
2555 #include <isl/aff.h>
2556 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2557 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2558 __isl_keep isl_aff *aff2);
2562 #include <isl/aff.h>
2563 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2564 __isl_take isl_aff *aff2);
2565 __isl_give isl_pw_aff *isl_pw_aff_add(
2566 __isl_take isl_pw_aff *pwaff1,
2567 __isl_take isl_pw_aff *pwaff2);
2568 __isl_give isl_pw_aff *isl_pw_aff_min(
2569 __isl_take isl_pw_aff *pwaff1,
2570 __isl_take isl_pw_aff *pwaff2);
2571 __isl_give isl_pw_aff *isl_pw_aff_max(
2572 __isl_take isl_pw_aff *pwaff1,
2573 __isl_take isl_pw_aff *pwaff2);
2574 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2575 __isl_take isl_aff *aff2);
2576 __isl_give isl_pw_aff *isl_pw_aff_sub(
2577 __isl_take isl_pw_aff *pwaff1,
2578 __isl_take isl_pw_aff *pwaff2);
2579 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2580 __isl_give isl_pw_aff *isl_pw_aff_neg(
2581 __isl_take isl_pw_aff *pwaff);
2582 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2583 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2584 __isl_take isl_pw_aff *pwaff);
2585 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2586 __isl_give isl_pw_aff *isl_pw_aff_floor(
2587 __isl_take isl_pw_aff *pwaff);
2588 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2590 __isl_give isl_pw_aff *isl_pw_aff_mod(
2591 __isl_take isl_pw_aff *pwaff, isl_int mod);
2592 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2594 __isl_give isl_pw_aff *isl_pw_aff_scale(
2595 __isl_take isl_pw_aff *pwaff, isl_int f);
2596 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2598 __isl_give isl_aff *isl_aff_scale_down_ui(
2599 __isl_take isl_aff *aff, unsigned f);
2600 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2601 __isl_take isl_pw_aff *pwaff, isl_int f);
2603 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2604 __isl_take isl_pw_aff_list *list);
2605 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2606 __isl_take isl_pw_aff_list *list);
2608 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2609 __isl_take isl_pw_aff *pwqp);
2611 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2612 __isl_take isl_pw_aff *pwaff,
2613 __isl_take isl_dim *model);
2615 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2616 __isl_take isl_set *context);
2617 __isl_give isl_pw_aff *isl_pw_aff_gist(
2618 __isl_take isl_pw_aff *pwaff,
2619 __isl_take isl_set *context);
2621 __isl_give isl_set *isl_pw_aff_domain(
2622 __isl_take isl_pw_aff *pwaff);
2624 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2625 __isl_take isl_aff *aff2);
2626 __isl_give isl_pw_aff *isl_pw_aff_mul(
2627 __isl_take isl_pw_aff *pwaff1,
2628 __isl_take isl_pw_aff *pwaff2);
2630 When multiplying two affine expressions, at least one of the two needs
2633 #include <isl/aff.h>
2634 __isl_give isl_basic_set *isl_aff_le_basic_set(
2635 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2636 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2637 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2638 __isl_give isl_set *isl_pw_aff_eq_set(
2639 __isl_take isl_pw_aff *pwaff1,
2640 __isl_take isl_pw_aff *pwaff2);
2641 __isl_give isl_set *isl_pw_aff_ne_set(
2642 __isl_take isl_pw_aff *pwaff1,
2643 __isl_take isl_pw_aff *pwaff2);
2644 __isl_give isl_set *isl_pw_aff_le_set(
2645 __isl_take isl_pw_aff *pwaff1,
2646 __isl_take isl_pw_aff *pwaff2);
2647 __isl_give isl_set *isl_pw_aff_lt_set(
2648 __isl_take isl_pw_aff *pwaff1,
2649 __isl_take isl_pw_aff *pwaff2);
2650 __isl_give isl_set *isl_pw_aff_ge_set(
2651 __isl_take isl_pw_aff *pwaff1,
2652 __isl_take isl_pw_aff *pwaff2);
2653 __isl_give isl_set *isl_pw_aff_gt_set(
2654 __isl_take isl_pw_aff *pwaff1,
2655 __isl_take isl_pw_aff *pwaff2);
2657 __isl_give isl_set *isl_pw_aff_list_eq_set(
2658 __isl_take isl_pw_aff_list *list1,
2659 __isl_take isl_pw_aff_list *list2);
2660 __isl_give isl_set *isl_pw_aff_list_ne_set(
2661 __isl_take isl_pw_aff_list *list1,
2662 __isl_take isl_pw_aff_list *list2);
2663 __isl_give isl_set *isl_pw_aff_list_le_set(
2664 __isl_take isl_pw_aff_list *list1,
2665 __isl_take isl_pw_aff_list *list2);
2666 __isl_give isl_set *isl_pw_aff_list_lt_set(
2667 __isl_take isl_pw_aff_list *list1,
2668 __isl_take isl_pw_aff_list *list2);
2669 __isl_give isl_set *isl_pw_aff_list_ge_set(
2670 __isl_take isl_pw_aff_list *list1,
2671 __isl_take isl_pw_aff_list *list2);
2672 __isl_give isl_set *isl_pw_aff_list_gt_set(
2673 __isl_take isl_pw_aff_list *list1,
2674 __isl_take isl_pw_aff_list *list2);
2676 The function C<isl_aff_ge_basic_set> returns a basic set
2677 containing those elements in the shared space
2678 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2679 The function C<isl_aff_ge_set> returns a set
2680 containing those elements in the shared domain
2681 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2682 The functions operating on C<isl_pw_aff_list> apply the corresponding
2683 C<isl_pw_aff> function to each pair of elements in the two lists.
2685 #include <isl/aff.h>
2686 __isl_give isl_set *isl_pw_aff_nonneg_set(
2687 __isl_take isl_pw_aff *pwaff);
2688 __isl_give isl_set *isl_pw_aff_zero_set(
2689 __isl_take isl_pw_aff *pwaff);
2690 __isl_give isl_set *isl_pw_aff_non_zero_set(
2691 __isl_take isl_pw_aff *pwaff);
2693 The function C<isl_pw_aff_nonneg_set> returns a set
2694 containing those elements in the domain
2695 of C<pwaff> where C<pwaff> is non-negative.
2697 #include <isl/aff.h>
2698 __isl_give isl_pw_aff *isl_pw_aff_cond(
2699 __isl_take isl_set *cond,
2700 __isl_take isl_pw_aff *pwaff_true,
2701 __isl_take isl_pw_aff *pwaff_false);
2703 The function C<isl_pw_aff_cond> performs a conditional operator
2704 and returns an expression that is equal to C<pwaff_true>
2705 for elements in C<cond> and equal to C<pwaff_false> for elements
2708 #include <isl/aff.h>
2709 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2710 __isl_take isl_pw_aff *pwaff1,
2711 __isl_take isl_pw_aff *pwaff2);
2712 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2713 __isl_take isl_pw_aff *pwaff1,
2714 __isl_take isl_pw_aff *pwaff2);
2716 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2717 expression with a domain that is the union of those of C<pwaff1> and
2718 C<pwaff2> and such that on each cell, the quasi-affine expression is
2719 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2720 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2721 associated expression is the defined one.
2723 An expression can be printed using
2725 #include <isl/aff.h>
2726 __isl_give isl_printer *isl_printer_print_aff(
2727 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2729 __isl_give isl_printer *isl_printer_print_pw_aff(
2730 __isl_take isl_printer *p,
2731 __isl_keep isl_pw_aff *pwaff);
2735 Points are elements of a set. They can be used to construct
2736 simple sets (boxes) or they can be used to represent the
2737 individual elements of a set.
2738 The zero point (the origin) can be created using
2740 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2742 The coordinates of a point can be inspected, set and changed
2745 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2746 enum isl_dim_type type, int pos, isl_int *v);
2747 __isl_give isl_point *isl_point_set_coordinate(
2748 __isl_take isl_point *pnt,
2749 enum isl_dim_type type, int pos, isl_int v);
2751 __isl_give isl_point *isl_point_add_ui(
2752 __isl_take isl_point *pnt,
2753 enum isl_dim_type type, int pos, unsigned val);
2754 __isl_give isl_point *isl_point_sub_ui(
2755 __isl_take isl_point *pnt,
2756 enum isl_dim_type type, int pos, unsigned val);
2758 Other properties can be obtained using
2760 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2762 Points can be copied or freed using
2764 __isl_give isl_point *isl_point_copy(
2765 __isl_keep isl_point *pnt);
2766 void isl_point_free(__isl_take isl_point *pnt);
2768 A singleton set can be created from a point using
2770 __isl_give isl_basic_set *isl_basic_set_from_point(
2771 __isl_take isl_point *pnt);
2772 __isl_give isl_set *isl_set_from_point(
2773 __isl_take isl_point *pnt);
2775 and a box can be created from two opposite extremal points using
2777 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2778 __isl_take isl_point *pnt1,
2779 __isl_take isl_point *pnt2);
2780 __isl_give isl_set *isl_set_box_from_points(
2781 __isl_take isl_point *pnt1,
2782 __isl_take isl_point *pnt2);
2784 All elements of a B<bounded> (union) set can be enumerated using
2785 the following functions.
2787 int isl_set_foreach_point(__isl_keep isl_set *set,
2788 int (*fn)(__isl_take isl_point *pnt, void *user),
2790 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2791 int (*fn)(__isl_take isl_point *pnt, void *user),
2794 The function C<fn> is called for each integer point in
2795 C<set> with as second argument the last argument of
2796 the C<isl_set_foreach_point> call. The function C<fn>
2797 should return C<0> on success and C<-1> on failure.
2798 In the latter case, C<isl_set_foreach_point> will stop
2799 enumerating and return C<-1> as well.
2800 If the enumeration is performed successfully and to completion,
2801 then C<isl_set_foreach_point> returns C<0>.
2803 To obtain a single point of a (basic) set, use
2805 __isl_give isl_point *isl_basic_set_sample_point(
2806 __isl_take isl_basic_set *bset);
2807 __isl_give isl_point *isl_set_sample_point(
2808 __isl_take isl_set *set);
2810 If C<set> does not contain any (integer) points, then the
2811 resulting point will be ``void'', a property that can be
2814 int isl_point_is_void(__isl_keep isl_point *pnt);
2816 =head2 Piecewise Quasipolynomials
2818 A piecewise quasipolynomial is a particular kind of function that maps
2819 a parametric point to a rational value.
2820 More specifically, a quasipolynomial is a polynomial expression in greatest
2821 integer parts of affine expressions of parameters and variables.
2822 A piecewise quasipolynomial is a subdivision of a given parametric
2823 domain into disjoint cells with a quasipolynomial associated to
2824 each cell. The value of the piecewise quasipolynomial at a given
2825 point is the value of the quasipolynomial associated to the cell
2826 that contains the point. Outside of the union of cells,
2827 the value is assumed to be zero.
2828 For example, the piecewise quasipolynomial
2830 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2832 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2833 A given piecewise quasipolynomial has a fixed domain dimension.
2834 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2835 defined over different domains.
2836 Piecewise quasipolynomials are mainly used by the C<barvinok>
2837 library for representing the number of elements in a parametric set or map.
2838 For example, the piecewise quasipolynomial above represents
2839 the number of points in the map
2841 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2843 =head3 Printing (Piecewise) Quasipolynomials
2845 Quasipolynomials and piecewise quasipolynomials can be printed
2846 using the following functions.
2848 __isl_give isl_printer *isl_printer_print_qpolynomial(
2849 __isl_take isl_printer *p,
2850 __isl_keep isl_qpolynomial *qp);
2852 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2853 __isl_take isl_printer *p,
2854 __isl_keep isl_pw_qpolynomial *pwqp);
2856 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2857 __isl_take isl_printer *p,
2858 __isl_keep isl_union_pw_qpolynomial *upwqp);
2860 The output format of the printer
2861 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2862 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2864 In case of printing in C<ISL_FORMAT_C>, the user may want
2865 to set the names of all dimensions
2867 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2868 __isl_take isl_qpolynomial *qp,
2869 enum isl_dim_type type, unsigned pos,
2871 __isl_give isl_pw_qpolynomial *
2872 isl_pw_qpolynomial_set_dim_name(
2873 __isl_take isl_pw_qpolynomial *pwqp,
2874 enum isl_dim_type type, unsigned pos,
2877 =head3 Creating New (Piecewise) Quasipolynomials
2879 Some simple quasipolynomials can be created using the following functions.
2880 More complicated quasipolynomials can be created by applying
2881 operations such as addition and multiplication
2882 on the resulting quasipolynomials
2884 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2885 __isl_take isl_dim *dim);
2886 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2887 __isl_take isl_dim *dim);
2888 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2889 __isl_take isl_dim *dim);
2890 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2891 __isl_take isl_dim *dim);
2892 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2893 __isl_take isl_dim *dim);
2894 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2895 __isl_take isl_dim *dim,
2896 const isl_int n, const isl_int d);
2897 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2898 __isl_take isl_div *div);
2899 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2900 __isl_take isl_dim *dim,
2901 enum isl_dim_type type, unsigned pos);
2902 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2903 __isl_take isl_aff *aff);
2905 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2906 with a single cell can be created using the following functions.
2907 Multiple of these single cell piecewise quasipolynomials can
2908 be combined to create more complicated piecewise quasipolynomials.
2910 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2911 __isl_take isl_dim *dim);
2912 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2913 __isl_take isl_set *set,
2914 __isl_take isl_qpolynomial *qp);
2915 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2916 __isl_take isl_qpolynomial *qp);
2917 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2918 __isl_take isl_pw_aff *pwaff);
2920 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2921 __isl_take isl_dim *dim);
2922 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2923 __isl_take isl_pw_qpolynomial *pwqp);
2924 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2925 __isl_take isl_union_pw_qpolynomial *upwqp,
2926 __isl_take isl_pw_qpolynomial *pwqp);
2928 Quasipolynomials can be copied and freed again using the following
2931 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2932 __isl_keep isl_qpolynomial *qp);
2933 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2935 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2936 __isl_keep isl_pw_qpolynomial *pwqp);
2937 void *isl_pw_qpolynomial_free(
2938 __isl_take isl_pw_qpolynomial *pwqp);
2940 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2941 __isl_keep isl_union_pw_qpolynomial *upwqp);
2942 void isl_union_pw_qpolynomial_free(
2943 __isl_take isl_union_pw_qpolynomial *upwqp);
2945 =head3 Inspecting (Piecewise) Quasipolynomials
2947 To iterate over all piecewise quasipolynomials in a union
2948 piecewise quasipolynomial, use the following function
2950 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2951 __isl_keep isl_union_pw_qpolynomial *upwqp,
2952 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2955 To extract the piecewise quasipolynomial from a union with a given dimension
2958 __isl_give isl_pw_qpolynomial *
2959 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2960 __isl_keep isl_union_pw_qpolynomial *upwqp,
2961 __isl_take isl_dim *dim);
2963 To iterate over the cells in a piecewise quasipolynomial,
2964 use either of the following two functions
2966 int isl_pw_qpolynomial_foreach_piece(
2967 __isl_keep isl_pw_qpolynomial *pwqp,
2968 int (*fn)(__isl_take isl_set *set,
2969 __isl_take isl_qpolynomial *qp,
2970 void *user), void *user);
2971 int isl_pw_qpolynomial_foreach_lifted_piece(
2972 __isl_keep isl_pw_qpolynomial *pwqp,
2973 int (*fn)(__isl_take isl_set *set,
2974 __isl_take isl_qpolynomial *qp,
2975 void *user), void *user);
2977 As usual, the function C<fn> should return C<0> on success
2978 and C<-1> on failure. The difference between
2979 C<isl_pw_qpolynomial_foreach_piece> and
2980 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2981 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2982 compute unique representations for all existentially quantified
2983 variables and then turn these existentially quantified variables
2984 into extra set variables, adapting the associated quasipolynomial
2985 accordingly. This means that the C<set> passed to C<fn>
2986 will not have any existentially quantified variables, but that
2987 the dimensions of the sets may be different for different
2988 invocations of C<fn>.
2990 To iterate over all terms in a quasipolynomial,
2993 int isl_qpolynomial_foreach_term(
2994 __isl_keep isl_qpolynomial *qp,
2995 int (*fn)(__isl_take isl_term *term,
2996 void *user), void *user);
2998 The terms themselves can be inspected and freed using
3001 unsigned isl_term_dim(__isl_keep isl_term *term,
3002 enum isl_dim_type type);
3003 void isl_term_get_num(__isl_keep isl_term *term,
3005 void isl_term_get_den(__isl_keep isl_term *term,
3007 int isl_term_get_exp(__isl_keep isl_term *term,
3008 enum isl_dim_type type, unsigned pos);
3009 __isl_give isl_div *isl_term_get_div(
3010 __isl_keep isl_term *term, unsigned pos);
3011 void isl_term_free(__isl_take isl_term *term);
3013 Each term is a product of parameters, set variables and
3014 integer divisions. The function C<isl_term_get_exp>
3015 returns the exponent of a given dimensions in the given term.
3016 The C<isl_int>s in the arguments of C<isl_term_get_num>
3017 and C<isl_term_get_den> need to have been initialized
3018 using C<isl_int_init> before calling these functions.
3020 =head3 Properties of (Piecewise) Quasipolynomials
3022 To check whether a quasipolynomial is actually a constant,
3023 use the following function.
3025 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3026 isl_int *n, isl_int *d);
3028 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3029 then the numerator and denominator of the constant
3030 are returned in C<*n> and C<*d>, respectively.
3032 =head3 Operations on (Piecewise) Quasipolynomials
3034 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3035 __isl_take isl_qpolynomial *qp, isl_int v);
3036 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3037 __isl_take isl_qpolynomial *qp);
3038 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3039 __isl_take isl_qpolynomial *qp1,
3040 __isl_take isl_qpolynomial *qp2);
3041 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3042 __isl_take isl_qpolynomial *qp1,
3043 __isl_take isl_qpolynomial *qp2);
3044 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3045 __isl_take isl_qpolynomial *qp1,
3046 __isl_take isl_qpolynomial *qp2);
3047 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3048 __isl_take isl_qpolynomial *qp, unsigned exponent);
3050 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3051 __isl_take isl_pw_qpolynomial *pwqp1,
3052 __isl_take isl_pw_qpolynomial *pwqp2);
3053 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3054 __isl_take isl_pw_qpolynomial *pwqp1,
3055 __isl_take isl_pw_qpolynomial *pwqp2);
3056 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3057 __isl_take isl_pw_qpolynomial *pwqp1,
3058 __isl_take isl_pw_qpolynomial *pwqp2);
3059 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3060 __isl_take isl_pw_qpolynomial *pwqp);
3061 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3062 __isl_take isl_pw_qpolynomial *pwqp1,
3063 __isl_take isl_pw_qpolynomial *pwqp2);
3064 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3065 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3067 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3068 __isl_take isl_union_pw_qpolynomial *upwqp1,
3069 __isl_take isl_union_pw_qpolynomial *upwqp2);
3070 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3071 __isl_take isl_union_pw_qpolynomial *upwqp1,
3072 __isl_take isl_union_pw_qpolynomial *upwqp2);
3073 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3074 __isl_take isl_union_pw_qpolynomial *upwqp1,
3075 __isl_take isl_union_pw_qpolynomial *upwqp2);
3077 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3078 __isl_take isl_pw_qpolynomial *pwqp,
3079 __isl_take isl_point *pnt);
3081 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3082 __isl_take isl_union_pw_qpolynomial *upwqp,
3083 __isl_take isl_point *pnt);
3085 __isl_give isl_set *isl_pw_qpolynomial_domain(
3086 __isl_take isl_pw_qpolynomial *pwqp);
3087 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3088 __isl_take isl_pw_qpolynomial *pwpq,
3089 __isl_take isl_set *set);
3091 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3092 __isl_take isl_union_pw_qpolynomial *upwqp);
3093 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3094 __isl_take isl_union_pw_qpolynomial *upwpq,
3095 __isl_take isl_union_set *uset);
3097 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3098 __isl_take isl_qpolynomial *qp,
3099 __isl_take isl_dim *model);
3101 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3102 __isl_take isl_union_pw_qpolynomial *upwqp);
3104 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3105 __isl_take isl_qpolynomial *qp,
3106 __isl_take isl_set *context);
3108 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3109 __isl_take isl_pw_qpolynomial *pwqp,
3110 __isl_take isl_set *context);
3112 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3113 __isl_take isl_union_pw_qpolynomial *upwqp,
3114 __isl_take isl_union_set *context);
3116 The gist operation applies the gist operation to each of
3117 the cells in the domain of the input piecewise quasipolynomial.
3118 The context is also exploited
3119 to simplify the quasipolynomials associated to each cell.
3121 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3122 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3123 __isl_give isl_union_pw_qpolynomial *
3124 isl_union_pw_qpolynomial_to_polynomial(
3125 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3127 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3128 the polynomial will be an overapproximation. If C<sign> is negative,
3129 it will be an underapproximation. If C<sign> is zero, the approximation
3130 will lie somewhere in between.
3132 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3134 A piecewise quasipolynomial reduction is a piecewise
3135 reduction (or fold) of quasipolynomials.
3136 In particular, the reduction can be maximum or a minimum.
3137 The objects are mainly used to represent the result of
3138 an upper or lower bound on a quasipolynomial over its domain,
3139 i.e., as the result of the following function.
3141 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3142 __isl_take isl_pw_qpolynomial *pwqp,
3143 enum isl_fold type, int *tight);
3145 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3146 __isl_take isl_union_pw_qpolynomial *upwqp,
3147 enum isl_fold type, int *tight);
3149 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3150 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3151 is the returned bound is known be tight, i.e., for each value
3152 of the parameters there is at least
3153 one element in the domain that reaches the bound.
3154 If the domain of C<pwqp> is not wrapping, then the bound is computed
3155 over all elements in that domain and the result has a purely parametric
3156 domain. If the domain of C<pwqp> is wrapping, then the bound is
3157 computed over the range of the wrapped relation. The domain of the
3158 wrapped relation becomes the domain of the result.
3160 A (piecewise) quasipolynomial reduction can be copied or freed using the
3161 following functions.
3163 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3164 __isl_keep isl_qpolynomial_fold *fold);
3165 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3166 __isl_keep isl_pw_qpolynomial_fold *pwf);
3167 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3168 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3169 void isl_qpolynomial_fold_free(
3170 __isl_take isl_qpolynomial_fold *fold);
3171 void *isl_pw_qpolynomial_fold_free(
3172 __isl_take isl_pw_qpolynomial_fold *pwf);
3173 void isl_union_pw_qpolynomial_fold_free(
3174 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3176 =head3 Printing Piecewise Quasipolynomial Reductions
3178 Piecewise quasipolynomial reductions can be printed
3179 using the following function.
3181 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3182 __isl_take isl_printer *p,
3183 __isl_keep isl_pw_qpolynomial_fold *pwf);
3184 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3185 __isl_take isl_printer *p,
3186 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3188 For C<isl_printer_print_pw_qpolynomial_fold>,
3189 output format of the printer
3190 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3191 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3192 output format of the printer
3193 needs to be set to C<ISL_FORMAT_ISL>.
3194 In case of printing in C<ISL_FORMAT_C>, the user may want
3195 to set the names of all dimensions
3197 __isl_give isl_pw_qpolynomial_fold *
3198 isl_pw_qpolynomial_fold_set_dim_name(
3199 __isl_take isl_pw_qpolynomial_fold *pwf,
3200 enum isl_dim_type type, unsigned pos,
3203 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3205 To iterate over all piecewise quasipolynomial reductions in a union
3206 piecewise quasipolynomial reduction, use the following function
3208 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3209 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3210 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3211 void *user), void *user);
3213 To iterate over the cells in a piecewise quasipolynomial reduction,
3214 use either of the following two functions
3216 int isl_pw_qpolynomial_fold_foreach_piece(
3217 __isl_keep isl_pw_qpolynomial_fold *pwf,
3218 int (*fn)(__isl_take isl_set *set,
3219 __isl_take isl_qpolynomial_fold *fold,
3220 void *user), void *user);
3221 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3222 __isl_keep isl_pw_qpolynomial_fold *pwf,
3223 int (*fn)(__isl_take isl_set *set,
3224 __isl_take isl_qpolynomial_fold *fold,
3225 void *user), void *user);
3227 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3228 of the difference between these two functions.
3230 To iterate over all quasipolynomials in a reduction, use
3232 int isl_qpolynomial_fold_foreach_qpolynomial(
3233 __isl_keep isl_qpolynomial_fold *fold,
3234 int (*fn)(__isl_take isl_qpolynomial *qp,
3235 void *user), void *user);
3237 =head3 Operations on Piecewise Quasipolynomial Reductions
3239 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3240 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3242 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3243 __isl_take isl_pw_qpolynomial_fold *pwf1,
3244 __isl_take isl_pw_qpolynomial_fold *pwf2);
3246 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3247 __isl_take isl_pw_qpolynomial_fold *pwf1,
3248 __isl_take isl_pw_qpolynomial_fold *pwf2);
3250 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3251 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3252 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3254 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3255 __isl_take isl_pw_qpolynomial_fold *pwf,
3256 __isl_take isl_point *pnt);
3258 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3259 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3260 __isl_take isl_point *pnt);
3262 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3263 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3264 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3265 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3266 __isl_take isl_union_set *uset);
3268 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3269 __isl_take isl_pw_qpolynomial_fold *pwf);
3271 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3272 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3274 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3275 __isl_take isl_pw_qpolynomial_fold *pwf,
3276 __isl_take isl_set *context);
3278 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3279 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3280 __isl_take isl_union_set *context);
3282 The gist operation applies the gist operation to each of
3283 the cells in the domain of the input piecewise quasipolynomial reduction.
3284 In future, the operation will also exploit the context
3285 to simplify the quasipolynomial reductions associated to each cell.
3287 __isl_give isl_pw_qpolynomial_fold *
3288 isl_set_apply_pw_qpolynomial_fold(
3289 __isl_take isl_set *set,
3290 __isl_take isl_pw_qpolynomial_fold *pwf,
3292 __isl_give isl_pw_qpolynomial_fold *
3293 isl_map_apply_pw_qpolynomial_fold(
3294 __isl_take isl_map *map,
3295 __isl_take isl_pw_qpolynomial_fold *pwf,
3297 __isl_give isl_union_pw_qpolynomial_fold *
3298 isl_union_set_apply_union_pw_qpolynomial_fold(
3299 __isl_take isl_union_set *uset,
3300 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3302 __isl_give isl_union_pw_qpolynomial_fold *
3303 isl_union_map_apply_union_pw_qpolynomial_fold(
3304 __isl_take isl_union_map *umap,
3305 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3308 The functions taking a map
3309 compose the given map with the given piecewise quasipolynomial reduction.
3310 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3311 over all elements in the intersection of the range of the map
3312 and the domain of the piecewise quasipolynomial reduction
3313 as a function of an element in the domain of the map.
3314 The functions taking a set compute a bound over all elements in the
3315 intersection of the set and the domain of the
3316 piecewise quasipolynomial reduction.
3318 =head2 Dependence Analysis
3320 C<isl> contains specialized functionality for performing
3321 array dataflow analysis. That is, given a I<sink> access relation
3322 and a collection of possible I<source> access relations,
3323 C<isl> can compute relations that describe
3324 for each iteration of the sink access, which iteration
3325 of which of the source access relations was the last
3326 to access the same data element before the given iteration
3328 To compute standard flow dependences, the sink should be
3329 a read, while the sources should be writes.
3330 If any of the source accesses are marked as being I<may>
3331 accesses, then there will be a dependence to the last
3332 I<must> access B<and> to any I<may> access that follows
3333 this last I<must> access.
3334 In particular, if I<all> sources are I<may> accesses,
3335 then memory based dependence analysis is performed.
3336 If, on the other hand, all sources are I<must> accesses,
3337 then value based dependence analysis is performed.
3339 #include <isl/flow.h>
3341 typedef int (*isl_access_level_before)(void *first, void *second);
3343 __isl_give isl_access_info *isl_access_info_alloc(
3344 __isl_take isl_map *sink,
3345 void *sink_user, isl_access_level_before fn,
3347 __isl_give isl_access_info *isl_access_info_add_source(
3348 __isl_take isl_access_info *acc,
3349 __isl_take isl_map *source, int must,
3351 void isl_access_info_free(__isl_take isl_access_info *acc);
3353 __isl_give isl_flow *isl_access_info_compute_flow(
3354 __isl_take isl_access_info *acc);
3356 int isl_flow_foreach(__isl_keep isl_flow *deps,
3357 int (*fn)(__isl_take isl_map *dep, int must,
3358 void *dep_user, void *user),
3360 __isl_give isl_map *isl_flow_get_no_source(
3361 __isl_keep isl_flow *deps, int must);
3362 void isl_flow_free(__isl_take isl_flow *deps);
3364 The function C<isl_access_info_compute_flow> performs the actual
3365 dependence analysis. The other functions are used to construct
3366 the input for this function or to read off the output.
3368 The input is collected in an C<isl_access_info>, which can
3369 be created through a call to C<isl_access_info_alloc>.
3370 The arguments to this functions are the sink access relation
3371 C<sink>, a token C<sink_user> used to identify the sink
3372 access to the user, a callback function for specifying the
3373 relative order of source and sink accesses, and the number
3374 of source access relations that will be added.
3375 The callback function has type C<int (*)(void *first, void *second)>.
3376 The function is called with two user supplied tokens identifying
3377 either a source or the sink and it should return the shared nesting
3378 level and the relative order of the two accesses.
3379 In particular, let I<n> be the number of loops shared by
3380 the two accesses. If C<first> precedes C<second> textually,
3381 then the function should return I<2 * n + 1>; otherwise,
3382 it should return I<2 * n>.
3383 The sources can be added to the C<isl_access_info> by performing
3384 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3385 C<must> indicates whether the source is a I<must> access
3386 or a I<may> access. Note that a multi-valued access relation
3387 should only be marked I<must> if every iteration in the domain
3388 of the relation accesses I<all> elements in its image.
3389 The C<source_user> token is again used to identify
3390 the source access. The range of the source access relation
3391 C<source> should have the same dimension as the range
3392 of the sink access relation.
3393 The C<isl_access_info_free> function should usually not be
3394 called explicitly, because it is called implicitly by
3395 C<isl_access_info_compute_flow>.
3397 The result of the dependence analysis is collected in an
3398 C<isl_flow>. There may be elements of
3399 the sink access for which no preceding source access could be
3400 found or for which all preceding sources are I<may> accesses.
3401 The relations containing these elements can be obtained through
3402 calls to C<isl_flow_get_no_source>, the first with C<must> set
3403 and the second with C<must> unset.
3404 In the case of standard flow dependence analysis,
3405 with the sink a read and the sources I<must> writes,
3406 the first relation corresponds to the reads from uninitialized
3407 array elements and the second relation is empty.
3408 The actual flow dependences can be extracted using
3409 C<isl_flow_foreach>. This function will call the user-specified
3410 callback function C<fn> for each B<non-empty> dependence between
3411 a source and the sink. The callback function is called
3412 with four arguments, the actual flow dependence relation
3413 mapping source iterations to sink iterations, a boolean that
3414 indicates whether it is a I<must> or I<may> dependence, a token
3415 identifying the source and an additional C<void *> with value
3416 equal to the third argument of the C<isl_flow_foreach> call.
3417 A dependence is marked I<must> if it originates from a I<must>
3418 source and if it is not followed by any I<may> sources.
3420 After finishing with an C<isl_flow>, the user should call
3421 C<isl_flow_free> to free all associated memory.
3423 A higher-level interface to dependence analysis is provided
3424 by the following function.
3426 #include <isl/flow.h>
3428 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3429 __isl_take isl_union_map *must_source,
3430 __isl_take isl_union_map *may_source,
3431 __isl_take isl_union_map *schedule,
3432 __isl_give isl_union_map **must_dep,
3433 __isl_give isl_union_map **may_dep,
3434 __isl_give isl_union_map **must_no_source,
3435 __isl_give isl_union_map **may_no_source);
3437 The arrays are identified by the tuple names of the ranges
3438 of the accesses. The iteration domains by the tuple names
3439 of the domains of the accesses and of the schedule.
3440 The relative order of the iteration domains is given by the
3441 schedule. The relations returned through C<must_no_source>
3442 and C<may_no_source> are subsets of C<sink>.
3443 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3444 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3445 any of the other arguments is treated as an error.
3449 B<The functionality described in this section is fairly new
3450 and may be subject to change.>
3452 The following function can be used to compute a schedule
3453 for a union of domains. The generated schedule respects
3454 all C<validity> dependences. That is, all dependence distances
3455 over these dependences in the scheduled space are lexicographically
3456 positive. The generated schedule schedule also tries to minimize
3457 the dependence distances over C<proximity> dependences.
3458 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3459 for groups of domains where the dependence distances have only
3460 non-negative values.
3461 The algorithm used to construct the schedule is similar to that
3464 #include <isl/schedule.h>
3465 __isl_give isl_schedule *isl_union_set_compute_schedule(
3466 __isl_take isl_union_set *domain,
3467 __isl_take isl_union_map *validity,
3468 __isl_take isl_union_map *proximity);
3469 void *isl_schedule_free(__isl_take isl_schedule *sched);
3471 A mapping from the domains to the scheduled space can be obtained
3472 from an C<isl_schedule> using the following function.
3474 __isl_give isl_union_map *isl_schedule_get_map(
3475 __isl_keep isl_schedule *sched);
3477 A representation of the schedule can be printed using
3479 __isl_give isl_printer *isl_printer_print_schedule(
3480 __isl_take isl_printer *p,
3481 __isl_keep isl_schedule *schedule);
3483 A representation of the schedule as a forest of bands can be obtained
3484 using the following function.
3486 __isl_give isl_band_list *isl_schedule_get_band_forest(
3487 __isl_keep isl_schedule *schedule);
3489 The list can be manipulated as explained in L<"Lists">.
3490 The bands inside the list can be copied and freed using the following
3493 #include <isl/band.h>
3494 __isl_give isl_band *isl_band_copy(
3495 __isl_keep isl_band *band);
3496 void *isl_band_free(__isl_take isl_band *band);
3498 Each band contains zero or more scheduling dimensions.
3499 These are referred to as the members of the band.
3500 The section of the schedule that corresponds to the band is
3501 referred to as the partial schedule of the band.
3502 For those nodes that participate in a band, the outer scheduling
3503 dimensions form the prefix schedule, while the inner scheduling
3504 dimensions form the suffix schedule.
3505 That is, if we take a cut of the band forest, then the union of
3506 the concatenations of the prefix, partial and suffix schedules of
3507 each band in the cut is equal to the entire schedule (modulo
3508 some possible padding at the end with zero scheduling dimensions).
3509 The properties of a band can be inspected using the following functions.
3511 #include <isl/band.h>
3512 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3514 int isl_band_has_children(__isl_keep isl_band *band);
3515 __isl_give isl_band_list *isl_band_get_children(
3516 __isl_keep isl_band *band);
3518 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3519 __isl_keep isl_band *band);
3520 __isl_give isl_union_map *isl_band_get_partial_schedule(
3521 __isl_keep isl_band *band);
3522 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3523 __isl_keep isl_band *band);
3525 int isl_band_n_member(__isl_keep isl_band *band);
3526 int isl_band_member_is_zero_distance(
3527 __isl_keep isl_band *band, int pos);
3529 Note that a scheduling dimension is considered to be ``zero
3530 distance'' if it does not carry any proximity dependences
3532 That is, if the dependence distances of the proximity
3533 dependences are all zero in that direction (for fixed
3534 iterations of outer bands).
3536 A representation of the band can be printed using
3538 #include <isl/band.h>
3539 __isl_give isl_printer *isl_printer_print_band(
3540 __isl_take isl_printer *p,
3541 __isl_keep isl_band *band);
3543 =head2 Parametric Vertex Enumeration
3545 The parametric vertex enumeration described in this section
3546 is mainly intended to be used internally and by the C<barvinok>
3549 #include <isl/vertices.h>
3550 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3551 __isl_keep isl_basic_set *bset);
3553 The function C<isl_basic_set_compute_vertices> performs the
3554 actual computation of the parametric vertices and the chamber
3555 decomposition and store the result in an C<isl_vertices> object.
3556 This information can be queried by either iterating over all
3557 the vertices or iterating over all the chambers or cells
3558 and then iterating over all vertices that are active on the chamber.
3560 int isl_vertices_foreach_vertex(
3561 __isl_keep isl_vertices *vertices,
3562 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3565 int isl_vertices_foreach_cell(
3566 __isl_keep isl_vertices *vertices,
3567 int (*fn)(__isl_take isl_cell *cell, void *user),
3569 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3570 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3573 Other operations that can be performed on an C<isl_vertices> object are
3576 isl_ctx *isl_vertices_get_ctx(
3577 __isl_keep isl_vertices *vertices);
3578 int isl_vertices_get_n_vertices(
3579 __isl_keep isl_vertices *vertices);
3580 void isl_vertices_free(__isl_take isl_vertices *vertices);
3582 Vertices can be inspected and destroyed using the following functions.
3584 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3585 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3586 __isl_give isl_basic_set *isl_vertex_get_domain(
3587 __isl_keep isl_vertex *vertex);
3588 __isl_give isl_basic_set *isl_vertex_get_expr(
3589 __isl_keep isl_vertex *vertex);
3590 void isl_vertex_free(__isl_take isl_vertex *vertex);
3592 C<isl_vertex_get_expr> returns a singleton parametric set describing
3593 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3595 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3596 B<rational> basic sets, so they should mainly be used for inspection
3597 and should not be mixed with integer sets.
3599 Chambers can be inspected and destroyed using the following functions.
3601 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3602 __isl_give isl_basic_set *isl_cell_get_domain(
3603 __isl_keep isl_cell *cell);
3604 void isl_cell_free(__isl_take isl_cell *cell);
3608 Although C<isl> is mainly meant to be used as a library,
3609 it also contains some basic applications that use some
3610 of the functionality of C<isl>.
3611 The input may be specified in either the L<isl format>
3612 or the L<PolyLib format>.
3614 =head2 C<isl_polyhedron_sample>
3616 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3617 an integer element of the polyhedron, if there is any.
3618 The first column in the output is the denominator and is always
3619 equal to 1. If the polyhedron contains no integer points,
3620 then a vector of length zero is printed.
3624 C<isl_pip> takes the same input as the C<example> program
3625 from the C<piplib> distribution, i.e., a set of constraints
3626 on the parameters, a line containing only -1 and finally a set
3627 of constraints on a parametric polyhedron.
3628 The coefficients of the parameters appear in the last columns
3629 (but before the final constant column).
3630 The output is the lexicographic minimum of the parametric polyhedron.
3631 As C<isl> currently does not have its own output format, the output
3632 is just a dump of the internal state.
3634 =head2 C<isl_polyhedron_minimize>
3636 C<isl_polyhedron_minimize> computes the minimum of some linear
3637 or affine objective function over the integer points in a polyhedron.
3638 If an affine objective function
3639 is given, then the constant should appear in the last column.
3641 =head2 C<isl_polytope_scan>
3643 Given a polytope, C<isl_polytope_scan> prints
3644 all integer points in the polytope.